MASTER'S IN FUNDAMENTAL PHYSICS AND APPLICATIONS

This module covers the fundamentals of the physics and technology of semiconductor-based components. Most of the course unit focuses on the physics of the components. Drawing on the equations that describe the properties of materials, the main types of junctions are examined (p/n, metal/semiconductor, MIS). Based on this knowledge, the operation of basic components (diodes, transistors) is explained. In the second part, the fundamental building blocks of component manufacturing processes are presented.

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English tutorial course for students in the Master's 1 Physics program who are working toward professional proficiency in scientific English.

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This course is one of the cornerstones of modern physics. It provides a body of knowledge that is strictly necessary for all physics tracks, as it lays the groundwork for the theoretical description of the interaction between the electromagnetic field and elementary quantum systems such as two-level systems, atoms, and molecules. It also provides the knowledge necessary for understanding lasers, modern optical devices, and spectroscopic methods and analyses.

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The purpose of this module is to enable students to compare experimental results with their theoretical knowledge. Particular attention is given to writing up results and presenting them in the form of oral presentations. The work is organized into an eight-hour session for which the students choose a topic. They record their results and analyses in a lab notebook modeled after the protocols used in laboratories. At the end of the semester, students select a topic, which they develop into a final report that they defend orally. This course serves as preparation for the internships students will complete during their program.

Examples of available experiments: optical spectroscopy (IR, visible), gamma, X-ray, and acoustic spectroscopy; low-temperature photoluminescence; near-field spectroscopy (AFM, STM); electron microscopy...

The range of experiments offered covers the areas of physics taught in the various physics tracks. Students must choose from among these experiments those that best align with their interests. Significant effort is made to incorporate new data-acquisition technologies and the use of computer tools to compare experimental results with theory.

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Through two specific examples (X-ray diffraction and vibrations), this module shows in detail how the physical properties of a solid are modeled. The formalism will also be applied to finite systems, such as nanoparticles, and will remain valid for amorphous materials; however, special attention will be given to periodic systems (ranging from linear chains to protein crystals, including graphene and silicon). The concept of reciprocal lattice will naturally arise in connection with this periodicity.

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This course unit covers a review and in-depth exploration of programming techniques, as well as an introduction to computational physics. We will begin with a review of procedural programming using Python 3. We will then take an in-depth look at numerical methods relevant to physics, studying a selection of classical algorithms from numerical analysis and applying them to physics problems.

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The EU course “Condensed Matter Physics 2: Electronic Properties” is intended for students interested in solid-state physics.

Following on from the course unit “Condensed Matter Physics 1: Structural Properties,” this course unit covers the properties of electrons in crystalline solids, the band structure of electronic energy levels, and the basic concepts of semiconductor physics.

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Modern experimental physics generally requires the setup of a data acquisition system of varying complexity involving different types of instruments—such as sources, sensors, actuators, etc.—and a controller (such as a computer). The objective of this course unit is to familiarize students with this type of problem so that they can set up such a data acquisition system. On the controller side, the control logic will be implemented in Python (specifically using the PyVisa library).  

- Overview of the most common communication interfaces/ports: serial (RS-232, USB), parallel (GPIB), and network (Ethernet) (CM).

- Implementation of simple examples of communication, device configuration, and data acquisition (lab).

- Development of a more comprehensive data acquisition system through projects (practical training). 

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This module focuses, on the one hand, on the physical understanding of light emission and absorption processes in semiconductor devices, and, on the other hand, on the technologies used to manufacture such devices. These topics are applied in the cleanroom project, which involves the fabrication and subsequent characterization of an optoelectronic component.

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Knowing how to collect and process data are essential skills in a scientific and/or technical professional setting. The objective of this course is to address, as effectively as possible, three types of standard professional skills:

· Advanced use of spreadsheets and graphing software (MS Excel, LO-CALC) for scientific and technical purposes

· Network interconnections: infrastructure, the TCP/IP protocol suite, security

· Introduction to relational databases (MS Access, LO-BASE) – concepts and terminology, creating queries, graphical reports, forms.

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Introductory Research Internship in a University Laboratory

Dates: May–June

Duration: 7 weeks minimum, extendable in July

Prior to the internship, analyzing an article recommended by the internship advisors helps prepare the student for the internship’s topic and for in-depth reading of scientific publications.

Following the internship, as part of a peer-review process, the student submits his or her written report and oral presentation for critical review by other students; it is the student’s responsibility to revise them accordingly before submitting the final versions to the internship committee.

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This course is designed to provide students with skills in the numerical solution of the Schrödinger equation in order to simulate complex quantum well structures. The course begins with a study of cases where the solution is analytical, followed by cases where the solution is semi-analytical, before moving on to the finite difference (FD) method. Various FD schemes are presented, each accompanied by an evaluation of convergence as a function of key parameters (domain truncation, number of samples, etc.). Finally, examples of concrete physical applications are examined.    

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This is the third and final part of the course series on the fabrication processes for micro-, nano-, and optoelectronic devices. The remaining technological building blocks not yet covered in previous semesters are presented in detail. The modeling and simulation aspects of these technological processes play a central role, serving as an introduction to TCAD solutions. Finally, a practical synthesis of all these topics is provided by demonstrating the sequence of all these technological steps required to produce discrete and integrated components, from the wafer to the packaged devices.

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This lecture unit presents the physical properties of various nanostructures, such as quantum wells, 1D photonic crystals, carbon nanotubes, and graphene. It covers their electronic (structure and transport), vibrational, and optical properties, as well as the radiation-matter interaction.

The goal will be to describe the development of low-dimensional materials and their associated electronic, photonic, and phononic structures, and to study transport phenomena, electron-photon and electron-phonon couplings, excitons, as well as the absorption, emission, and scattering of light.

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English tutorial course for students in the Master 2 Physics program who are preparing for a career in an English-speaking professional environment in a contemporary context.

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This module gives students the opportunity to learn about the unique aspects of the professional world and to prepare to enter it under the best possible conditions, particularly through sharing experiences with professionals in the field. Students practice successfully completing the job application process in a systematic manner by thoroughly analyzing job postings, crafting targeted resumes and cover letters, and preparing for job interviews (through role-playing and simulations).

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Experimental designs are part of the quality assurance process. It is a method for conducting tests and analyzing data that saves time and money. That is why it is so useful in industry.

The focus is on understanding the basics.

This is an interactive course that uses examples to illustrate concepts.

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This module aims to teach the operating principles of the main techniques used to characterize the structure (in volume and on the surface) and properties (optical, electronic, etc.) of condensed matter:

• X-ray and electron diffraction techniques
• optical spectroscopy techniques (absorption, reflection, luminescence)
• local probe microscopy

  This module aims to teach the operating principles of the main techniques used to characterize the structure (in volume and on the surface) and properties (optical, electronic, etc.) of condensed matter:

  • X-ray and electron diffraction techniques
  • optical spectroscopy techniques (absorption, reflection, luminescence)
  • local probe microscopy

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End-of-program internship, in a company or a university laboratory

The purpose of this significant professional experience (up to six months) is to demonstrate the student’s ability to hold management-level positions (engineer or doctoral researcher) or to pursue a doctoral degree in the fields covered by the program.

Start date: as early as February

Duration: four to six months, and must end before August 31.

End-of-program internship, in a company or a university laboratory

The purpose of this significant professional experience (up to six months) is to demonstrate the student’s ability to hold management-level positions (engineer or doctoral researcher) or to pursue a doctoral degree in the fields covered by the program.

Start date: as early as February

Duration: four to six months, and must end before August 31.

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This course is a hands-on training program in the main techniques of nanoscale characterization and nanotechnology:

• AFM
• SEM
• Photoluminescence
• X-ray diffraction
• Ellipsometry
• Optical Microscopy
• Source meter
• Capacitance Meter
• Manufacturing Processes for Microdevices in Cleanrooms

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This course describes the various detectors and the physical processes involved in particle detection in high-energy physics. Next, we will describe how the main particle accelerators work—not only in high-energy physics but also in many other fields, such as medicine, industry, materials science, archaeology, and more.

The course provides a detailed description of the physical processes and experimental techniques involved in the detection of charged and neutral particles in detectors, as these detections form the basis of all physical measurements.

We will provide a detailed description of the various types of radiation and particle-matter interactions.

We will focus on describing the methodologies associated with these processes as well as their statistical analysis.

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English tutorial course for students in the Master 2 Physics program who are preparing for a career in an English-speaking professional environment in a contemporary context.

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This course covers the essential fundamentals needed for a solid understanding of the physics of stellar atmospheres and stellar winds. The key elements of radiation transfer theory are covered, both in local thermodynamic equilibrium (LTE) and out of LTE, as well as the description of the gas (equation of state) and its interaction with the radiation field (opacities). Modern models and simulations are presented along with their application to determining stellar parameters—particularly chemical composition—through spectroscopy. The different types of stellar winds (pressure, radiative, and hybrid) are described using theories compared with observational data.

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During the “Observational Astrophysics 2” course, students must complete all stages of an observational astrophysics study. From defining the spectroscopic or photometric observations to be conducted during a four-night stay at the Haute-Provence Observatory, to modeling and critically discussing their measurements and writing a scientific report, students take an active role in this course.

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Interstellar Medium: Physicochemical Processes—Phases—Radioastronomy.

This course provides an introduction to the physicochemical processes relevant to the interstellar medium (dynamic, thermal, and chemical processes) as well as the associated observational techniques (molecular spectroscopy, radio astronomy). The main phases of the interstellar medium (ionized, atomic, and molecular phases) are also covered.

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This course provides a comprehensive overview of the Standard Model of particle physics. We will begin by studying the Dirac equation, the quantum description of the dynamics of a spin-½ particle. Next, we will examine how to describe electromagnetic interactions using quantum electrodynamics. Next, we will address weak interactions and their unified description with the electromagnetic interaction through the electroweak theory. Finally, we will study gauge theories and their spontaneous symmetry breaking in order to present the complete theory of the Standard Model of particle physics. To conclude, we will provide a brief overview of theories beyond the Standard Model.

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This course is an introduction to relativistic quantum field theory and its applications in particle physics. Using a scalar field as an example, we will develop the formalisms of canonical quantization and path integral quantization before introducing perturbation theory and some concepts of renormalization. We will discuss the quantization of spin-1/2 and spin-1 fields, concluding with a discussion of quantum electrodynamics.

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This course is an introduction to the standard model of cosmology, covering its theoretical and phenomenological aspects. It focuses on the hot inflationary Big Bang model. It builds on the M1 course in general relativity and cosmology.

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The lab exercises focus on the detection and measurement of cosmic rays (muons).

The goal will be to become familiar with a data acquisition system designed for measuring cosmic rays (primarily muons). Students will need to understand how the various components of the acquisition chain work individually (power supplies, photomultipliers, scintillators, discriminators, oscilloscopes, etc.) and then build their own acquisition system using these components. One objective of the system could be to determine the mass of the muon, but other applications are possible and are left to the students’ imagination.

Students will then need to collect data using their devices and analyze that data, taking into account the systematic and statistical errors in the dataset.

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This course describes the theoretical and observational foundations of the so-called cosmological dark matter problem. Dark matter manifests itself through gravitational effects at various astrophysical scales, ranging from the scale of galaxies to cosmological scales (the observable universe as a whole). It constitutes approximately 85% of the total matter in the universe, and it is impossible for it to be composed of the elementary particles that characterize ordinary, known matter. The course will focus in particular on potential solutions to this problem that connect the infinitely small (elementary particles) to the infinitely large (the large-scale universe).

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A 3- to 6-month internship (21 ECTS) in a laboratory designed to provide immersion in the world of research and preparation for the dissertation. This internship may be completed in a research laboratory in France or abroad. It runs from March¹ to May 31, the deadline for submitting the written report. An oral defense takes place in early June. The internship may be extended until August 31 in order to transition directly into the thesis. Topics cover a broad spectrum ranging from theoretical physics (cosmology, particle physics, and astroparticle physics) to experimental physics (LHC experiments, the search for gravitational waves or dark matter, large-field cosmological surveys, etc.).

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This course is an introduction to the acceleration, propagation, and radiation mechanisms of energetic particles in astrophysical media. It will cover the fundamental concepts in this field.

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The Observational Astrophysics 1 Workshop provides an introduction to conducting an observational study (photometry or spectroscopy) of astrophysical objects (stars, nebulae) at the M1 level. Students carry out every step of the process, from planning and conducting observations at the Faculty of Sciences’ astronomical observatory to calibrating and analyzing the data obtained. This module is designed to prepare students for the M2 module “Observational Astrophysics Workshop 2” (HAP905P).

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In this course, we study the theory of general relativity—that is, the modern description of universal gravitation. After a brief review of special relativity, we will familiarize ourselves with the basic concepts of general relativity by examining some accepted particular solutions to these equations in well-defined physical contexts: a weak field at the Earth’s surface, the geometry around an isolated spherical star, and the universe on large scales. This will allow us to generalize our understanding and construct the theory, then derive the field equations—that is, Einstein’s equations. The course will conclude with a discussion of black holes and gravitational waves.

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This course aims to provide a foundation in astronomy and astrophysics, which will be useful in the other astrophysics courses in the master’s program. It also illustrates how concepts from physics are applied to describe astrophysical objects. Most of the concepts covered here will be explored in greater depth later in the^second-year courses.

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Fluids are all around us at all times and on every scale. Understanding fluid mechanics means understanding the mechanics of our surroundings—air and water, in particular. As such, hydrodynamics is part of a physicist’s basic knowledge.

The course “Hydrodynamics” provides an introduction to the mechanics of ideal incompressible fluids (Euler) and Newtonian viscous fluids (Navier-Stokes). Classical flow patterns are presented, along with the concepts of the boundary layer, instability, and turbulence. The focus is on physical concepts rather than on advanced mathematical or numerical solution methods.

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English tutorial course for students in the Master's 1 Physics program who are working toward professional proficiency in scientific English.

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This course is one of the cornerstones of modern physics. It provides a body of knowledge that is strictly necessary for all physics tracks, as it lays the groundwork for the theoretical description of the interaction between the electromagnetic field and elementary quantum systems such as two-level systems, atoms, and molecules. It also provides the knowledge necessary for understanding lasers, modern optical devices, and spectroscopic methods and analyses.

View the full page

The purpose of this module is to enable students to compare experimental results with their theoretical knowledge. Particular attention is given to writing up results and presenting them in the form of oral presentations. The work is organized into an eight-hour session for which the students choose a topic. They record their results and analyses in a lab notebook modeled after the protocols used in laboratories. At the end of the semester, students select a topic, which they develop into a final report that they defend orally. This course serves as preparation for the internships students will complete during their program.

Examples of available experiments: optical spectroscopy (IR, visible), gamma, X-ray, and acoustic spectroscopy; low-temperature photoluminescence; near-field spectroscopy (AFM, STM); electron microscopy...

The range of experiments offered covers the areas of physics taught in the various physics tracks. Students must choose from among these experiments those that best align with their interests. Significant effort is made to incorporate new data-acquisition technologies and the use of computer tools to compare experimental results with theory.

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This course unit covers a review and in-depth exploration of programming techniques, as well as an introduction to computational physics. We will begin with a review of procedural programming using Python 3. We will then take an in-depth look at numerical methods relevant to physics, studying a selection of classical algorithms from numerical analysis and applying them to physics problems.

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This course is intended as an introduction to astroparticle physics (cosmic accelerators, gamma rays, multi-messenger phenomena, experimental techniques, etc.).

The course builds on the knowledge acquired in the third year of undergraduate studies to offer students a brief introduction to astroparticle physics. After a description of the general context, two examples of detectors used in gamma-ray astronomy will be discussed in detail, followed by an introduction to the physics of multi-messenger astrophysics (particularly through the detection of gravitational waves). The course will then address the physics of cosmic rays (CRs), the issues surrounding the acceleration and propagation of CRs, and the hypothesis that supernova remnants act as galactic accelerators of CRs (description of the first-order Fermi acceleration mechanism).

The course will conclude with a discussion of the cosmological challenges posed by future ground-based and space-based wide-field surveys (LSST and Euclid, in particular).

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This course is designed to introduce and develop several fundamental concepts and tools of non-relativistic quantum physics necessary for understanding the physical processes that describe the interactions between the elementary constituents of matter and radiation. We will also cover second quantization and the path integral formulation of quantum mechanics, which provide the ideal framework for the development of quantum field theory and its various applications (e.g., high-energy physics, condensed matter physics).

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Introduction to Advanced Statistical Physics: grand canonical ensemble; quantum statistics; quantum fluids (Bose-Einstein condensation, thermal radiation; Sommerfeld theory); phase transitions; Ising model; mean-field theory; dynamics of complex systems.

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This course is an introduction to the Standard Model of particle physics. We will begin by reviewing the elementary particles and their interactions. Next, we will examine how to use Lie group theory to classify these elementary particles. Finally, we will discuss the concept of electromagnetic interactions for charged particles without spin (scalar electrodynamics).

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Fluid mechanics is a fundamental tool for the sciences of the Universe: from Earth and the giant planets to stars, accretion disks, and the interstellar medium, it is an essential approach for studying astrophysical objects. The course unit “Fluid Dynamics in Astrophysics and Cosmology” builds upon the “Hydrodynamics” course unit and is organized around three central themes in astrophysics: rotating fluids, thermal convection, and magnetohydrodynamics.

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This 7-week internship (usually from around the end of April to the end of June) (10 ECTS) will provide students with their first exposure to the world of research in astrophysics, cosmology, or particle physics. Internships at the intersection of these disciplines—more commonly referred to as “astroparticle physics”—are also available. Internships may have a more theoretical or more experimental focus, depending on the choices of the students and their supervisors.

This internship can be completed at a research laboratory in France or abroad. However, it is traditionally carried out at one of the two UMRs at the University of Montpellier 2: the Montpellier Universe and Particles Laboratory (LUPM, IN2P3) or the Charles Coulomb Laboratory (L2C, INP).

The internship will allow the student to interact with a research team (national and/or international) and begin to explore the research topics they would most like to pursue in their future studies.

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Fluids are all around us at all times and on every scale. Understanding fluid mechanics means understanding the mechanics of our surroundings—air and water, in particular. As such, hydrodynamics is part of a physicist’s basic knowledge.

The course “Hydrodynamics” provides an introduction to the mechanics of ideal incompressible fluids (Euler) and Newtonian viscous fluids (Navier-Stokes). Classical flow patterns are presented, along with the concepts of the boundary layer, instability, and turbulence. The focus is on physical concepts rather than on advanced mathematical or numerical solution methods.

View the full page

English tutorial course for students in the Master's 1 Physics program who are working toward professional proficiency in scientific English.

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This course is one of the cornerstones of modern physics. It provides a body of knowledge that is strictly necessary for all physics tracks, as it lays the groundwork for the theoretical description of the interaction between the electromagnetic field and elementary quantum systems such as two-level systems, atoms, and molecules. It also provides the knowledge necessary for understanding lasers, modern optical devices, and spectroscopic methods and analyses.

View the full page

The purpose of this module is to enable students to compare experimental results with their theoretical knowledge. Particular attention is given to writing up results and presenting them in the form of oral presentations. The work is organized into an eight-hour session for which the students choose a topic. They record their results and analyses in a lab notebook modeled after the protocols used in laboratories. At the end of the semester, students select a topic, which they develop into a final report that they defend orally. This course serves as preparation for the internships students will complete during their program.

Examples of available experiments: optical spectroscopy (IR, visible), gamma, X-ray, and acoustic spectroscopy; low-temperature photoluminescence; near-field spectroscopy (AFM, STM); electron microscopy...

The range of experiments offered covers the areas of physics taught in the various physics tracks. Students must choose from among these experiments those that best align with their interests. Significant effort is made to incorporate new data-acquisition technologies and the use of computer tools to compare experimental results with theory.

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Through two specific examples (X-ray diffraction and vibrations), this module shows in detail how the physical properties of a solid are modeled. The formalism will also be applied to finite systems, such as nanoparticles, and will remain valid for amorphous materials; however, special attention will be given to periodic systems (ranging from linear chains to protein crystals, including graphene and silicon). The concept of reciprocal lattice will naturally arise in connection with this periodicity.

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The course aims to provide a general introduction to cellular and molecular biology and to contextualize the use of modern physics—through its quantitative methods and approaches—to describe biological systems and their complexity, from the molecular scale to the cellular and tissue scales.

Another fundamental topic covered is the quantification of phenomena, their physical interpretation, and their physical-mathematical modeling. The course provides an introduction to the philosophy and the full range of topics in this master’s program, which focuses on the study of the physical principles underlying the organization and dynamics of living and complex matter.

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This course unit covers a review and in-depth exploration of programming techniques, as well as an introduction to computational physics. We will begin with a review of procedural programming using Python 3. We will then take an in-depth look at numerical methods relevant to physics, studying a selection of classical algorithms from numerical analysis and applying them to physics problems.

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Introduction to Advanced Statistical Physics: grand canonical ensemble; quantum statistics; quantum fluids (Bose-Einstein condensation, thermal radiation; Sommerfeld theory); phase transitions; Ising model; mean-field theory; dynamics of complex systems.

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A 7-week laboratory internship designed to provide immersion in the world of research, whether basic and/or applied.

This internship can be completed in a research laboratory or technical facility in France or abroad.

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This course introduces the concepts, fundamentals, and orders of magnitude in the physics and physical chemistry of interfaces that govern the mesoscopic scale of matter and ultimately determine the behavior and properties of everyday objects—such as soil, milk, cheese, paints, inks, cosmetics, adhesives, lubricants, and many other technological processes—as well as biological cells and membranes.

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Knowing how to collect and process data are essential skills in a scientific and/or technical professional setting. The objective of this course is to address, as effectively as possible, three types of standard professional skills:

· Advanced use of spreadsheets and graphing software (MS Excel, LO-CALC) for scientific and technical purposes

· Network interconnections: infrastructure, the TCP/IP protocol suite, security

· Introduction to relational databases (MS Access, LO-BASE) – concepts and terminology, creating queries, graphical reports, forms.

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The word “biomimicry” comes from ancient Greek: bios (bios), meaning “life,” and mimesis, meaning “imitation.”

This term refers to the study of extracellular and intracellular biological phenomena using in vitro experimental techniques designed to reproduce—that is, to “mimic”—the characteristics of these phenomena, both qualitatively and quantitatively.

The biomimetic method approaches biological complexity “by subtraction”: by assembling new minimal systems (with a small number of parameters) under highly controlled conditions using abottom-up approach; by identifying the essential components; and by controlling the system’s parameters.

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This course introduces and develops various methods for modeling biological systems: from the physics of individual molecules to the physical study of systems and populations of objects (e.g., proteins) or organisms (bacteria).

These methods (both analytical and numerical) stem primarily from statistical physics, the theory of stochastic processes, and nonlinear physics.

Examples of studies are also provided based on the material covered in other modules in the M1 and M2 programs to contextualize the various examples within the framework of physical theory and quantitative experimentation on living matter.

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Polymer physics—to which this course serves as an introduction—focuses on the physical properties of covalently bonded chain-like assemblies ranging from a few dozen to a few million elementary molecules: polymers or macromolecules.

These synthetic or natural molecules can be observed in the solid state, liquid state, in solution, in a colloidal state, or confined to an interface.

Their highly distinctive physical properties have led to the development of specific theoretical tools and the emergence of this new branch of physics with numerous applications.

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English tutorial course for students in the Master 2 Physics program who are preparing for a career in an English-speaking professional environment in a contemporary context.

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This module gives students the opportunity to learn about the unique aspects of the professional world and to prepare to enter it under the best possible conditions, particularly through sharing experiences with professionals in the field. Students practice successfully completing the job application process in a systematic manner by thoroughly analyzing job postings, crafting targeted resumes and cover letters, and preparing for job interviews (through role-playing and simulations).

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This course unit provides an introduction to the field of complex fluids and active matter, with applications in both the physical chemistry of soft matter and the physics of living systems and biological objects.

It is common to both the PhyMV and SoftMat tracks.

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An internship lasting at least 5 months in a laboratory, designed to provide immersion in the world of research—both basic and/or applied—and to potentially prepare students for a doctoral dissertation. This internship may be completed in research laboratories and technical facilities in France or abroad.

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Fluids are all around us at all times and on every scale. Understanding fluid mechanics means understanding the mechanics of our surroundings—air and water, in particular. As such, hydrodynamics is part of a physicist’s basic knowledge.

The course “Hydrodynamics” provides an introduction to the mechanics of ideal incompressible fluids (Euler) and Newtonian viscous fluids (Navier-Stokes). Classical flow patterns are presented, along with the concepts of the boundary layer, instability, and turbulence. The focus is on physical concepts rather than on advanced mathematical or numerical solution methods.

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English tutorial course for students in the Master's 1 Physics program who are working toward professional proficiency in scientific English.

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This course is one of the cornerstones of modern physics. It provides a body of knowledge that is strictly necessary for all physics tracks, as it lays the groundwork for the theoretical description of the interaction between the electromagnetic field and elementary quantum systems such as two-level systems, atoms, and molecules. It also provides the knowledge necessary for understanding lasers, modern optical devices, and spectroscopic methods and analyses.

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Through two specific examples (X-ray diffraction and vibrations), this module shows in detail how the physical properties of a solid are modeled. The formalism will also be applied to finite systems, such as nanoparticles, and will remain valid for amorphous materials; however, special attention will be given to periodic systems (ranging from linear chains to protein crystals, including graphene and silicon). The concept of reciprocal lattice will naturally arise in connection with this periodicity.

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Introduction to Advanced Statistical Physics: grand canonical ensemble; quantum statistics; quantum fluids (Bose-Einstein condensation, thermal radiation; Sommerfeld theory); phase transitions; Ising model; mean-field theory; dynamics of complex systems.

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A 10-ECTS supervised project during which groups of students work on developing software for research or teaching.

This project is designed to give students their first semi-professional experience by working in groups of two or more on a fairly large-scale project, typically proposed by fellow researchers who wish to develop and/or expand software intended for research purposes or for the general public.

Supervision is provided by fellow physicists and, in some cases, computer scientists. Students submit their code along with documentation. A report is written, and an oral defense is held.    

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The EU course “Condensed Matter Physics 2: Electronic Properties” is intended for students interested in solid-state physics.

Following on from the course unit “Condensed Matter Physics 1: Structural Properties,” this course unit covers the properties of electrons in crystalline solids, the band structure of electronic energy levels, and the basic concepts of semiconductor physics.

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Modern experimental physics generally requires the setup of a data acquisition system of varying complexity involving different types of instruments—such as sources, sensors, actuators, etc.—and a controller (such as a computer). The objective of this course unit is to familiarize students with this type of problem so that they can set up such a data acquisition system. On the controller side, the control logic will be implemented in Python (specifically using the PyVisa library).  

- Overview of the most common communication interfaces/ports: serial (RS-232, USB), parallel (GPIB), and network (Ethernet) (CM).

- Implementation of simple examples of communication, device configuration, and data acquisition (lab).

- Development of a more comprehensive data acquisition system through projects (practical training). 

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Knowing how to collect and process data are essential skills in a scientific and/or technical professional setting. The objective of this course is to address, as effectively as possible, three types of standard professional skills:

· Advanced use of spreadsheets and graphing software (MS Excel, LO-CALC) for scientific and technical purposes

· Network interconnections: infrastructure, the TCP/IP protocol suite, security

· Introduction to relational databases (MS Access, LO-BASE) – concepts and terminology, creating queries, graphical reports, forms.

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Mathematics for Computational Physics. Introduction to tools for the study of partial differential equations (distributions, variational formulation, Sobolev spaces).

Introduction to integral methods and their numerical implementation. Applications to diffraction problems in the harmonic regime.

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This course is designed to provide students with skills in the numerical solution of the Schrödinger equation in order to simulate complex quantum well structures. The course begins with a study of cases where the solution is analytical, followed by cases where the solution is semi-analytical, before moving on to the finite difference (FD) method. Various FD schemes are presented, each accompanied by an evaluation of convergence as a function of key parameters (domain truncation, number of samples, etc.). Finally, examples of concrete physical applications are examined.    

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This course lays the groundwork for using “atomistic” simulation tools—that is, those based on microscopic interactions between constituents. Primarily, it lays the foundation for simulations known as “Molecular Dynamics” and “Monte Carlo.”

It covers the underlying theoretical concepts to build a solid understanding of the methods, as well as the practical implementation of the corresponding code.

The critical and reasoned analysis of data is also discussed.

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This course is an introductory course with no prerequisites on scientific image processing, in the context of both physics and the medical sciences.

Starting with the fundamentals of digital image coding, we will introduce the main techniques aimed first at improving image quality and then at extracting quantitative data from images. The course will cover deconvolution, noise reduction, thresholding, segmentation, Fourier transforms, and wavelets.

We will conclude by discussing the specific challenges posed by image sequences (films) or 3D images, such as MRI data in a medical context.

The tool used will be the MATLAB/Octave programming environment.

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This course is an introduction to artificial intelligence for physicists. It aims to explore applications of deep learning using the TensorFlow and Keras libraries. It includes a presentation of examples of how deep learning is used in physics.

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English tutorial course for students in the Master 2 Physics program who are preparing for a career in an English-speaking professional environment in a contemporary context.

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This module gives students the opportunity to learn about the unique aspects of the professional world and to prepare to enter it under the best possible conditions, particularly through sharing experiences with professionals in the field. Students practice successfully completing the job application process in a systematic manner by thoroughly analyzing job postings, crafting targeted resumes and cover letters, and preparing for job interviews (through role-playing and simulations).

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This course unit covers the computer-based solution of electromagnetism problems. Using Maxwell’s equations, it demonstrates how to simulate the behavior of electromagnetic waves in various media. In particular, it includes a detailed implementation of simulations based on the finite difference time domain (FDTD) method.

An introduction to diffraction problems in the harmonic regime caused by a bounded obstacle will be provided for the case of scalar waves in 2D and 3D.

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This module provides an introduction to advanced applications of atomistic simulation methods, particularly molecular dynamics.

It thus involves expanding on the methods already learned, both in the field of physics (ab initio simulations, density functional theory) and in terms of implementation (optimization, parallelization) and practical application (an introduction to conducting simulations in a high-performance computing environment).

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A 5-ECTS supervised project during which students work individually to develop software for research and development and/or teaching.

This project builds on the experience gained during the supervised project completed in the first year of the master’s program. This time, students work individually, which offers a different experience from the group-based project in the first year of the master’s program. Students are assigned the task of developing software that meets specific requirements and must deliver functional code.   

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A six-month M2 internship (25 ECTS) completed at a company or public organization (research laboratory, national agency, etc.).

The internship must focus on a physics problem that involves a numerical computation component.  

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This course will cover the main aspects of star and planetary system formation in two equal-length parts. The section on star formation will address the stability of clouds in equilibrium, the collapse of dense cores, protostars and their evolution, and the impact of young stars on their environment. Planetary formation will draw on constraints from the solar system and detections of exoplanets to address the structure and evolution of protoplanetary disks, as well as the formation of terrestrial planets and giant planets.

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English tutorial course for students in the Master 2 Physics program who are preparing for a career in an English-speaking professional environment in a contemporary context.

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This course covers the essential fundamentals needed for a solid understanding of the physics of stellar atmospheres and stellar winds. The key elements of radiation transfer theory are covered, both in local thermodynamic equilibrium (LTE) and out of LTE, as well as the description of the gas (equation of state) and its interaction with the radiation field (opacities). Modern models and simulations are presented along with their application to determining stellar parameters—particularly chemical composition—through spectroscopy. The different types of stellar winds (pressure, radiative, and hybrid) are described using theories compared with observational data.

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During the “Observational Astrophysics 2” course, students must complete all stages of an observational astrophysics study. From defining the spectroscopic or photometric observations to be conducted during a four-night stay at the Haute-Provence Observatory, to modeling and critically discussing their measurements and writing a scientific report, students take an active role in this course.

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The goal is to present the various observations and associated theoretical concepts—known as cosmological probes—that have helped establish the so-called “concordance” ΛCDM cosmological model. The course is divided into chapters of roughly equal length. It is supplemented by a series of seminars presented by students (flipped classroom) that delve deeper into more observational and technical aspects (based on a publication from a major collaboration).

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Interstellar Medium: Physicochemical Processes—Phases—Radioastronomy.

This course provides an introduction to the physicochemical processes relevant to the interstellar medium (dynamic, thermal, and chemical processes) as well as the associated observational techniques (molecular spectroscopy, radio astronomy). The main phases of the interstellar medium (ionized, atomic, and molecular phases) are also covered.

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This course lays the foundation for our understanding of the formation and evolution of galaxies, ranging from the astrophysical processes at play on small scales—such as star formation—to environmental effects on very large scales. A two-pronged approach will be used, focusing on both theoretical and observational aspects.

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Much of our understanding of the Universe relies on understanding and accurately modeling stars. Stars account for a very large portion of the total light emitted by galaxies, and they are major contributors to the chemical and dynamical evolution of galaxies. In this course, we will explore the physics underlying stellar structure and examine how this structure evolves over time in the case of isolated stars.

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A 4-month laboratory internship designed to provide immersion in the world of research and prepare students for their thesis.

This internship can be completed in a research laboratory in France or abroad.

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This course unit introduces astrophysical instruments and the signal processing tools used in their operation.

The focus is on instruments with high angular resolution and high contrast (interferometry, adaptive optics, coronography, etc.).

In addition, this course introduces the fundamentals of digital signal processing and presents a general methodology—based on the modeling of instrumental effects—for image reconstruction or the optimal analysis of measurements.

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Research in astrophysics draws on a variety of approaches (observations, theory, modeling, simulation), all of which rely on advanced computational tools.

To best prepare students in the M2 Astrophysics program for a research career, this module offers them—in a setting different from that of an internship—the opportunity to conduct an individual, supervised computational project on a topic proposed by a mentor, focusing on the use and/or development of professional-grade code to address a specific astrophysical question.

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This module covers the fundamentals of the physics and technology of semiconductor-based components. Most of the course unit focuses on the physics of the components. Drawing on the equations that describe the properties of materials, the main types of junctions are examined (p/n, metal/semiconductor, MIS). Based on this knowledge, the operation of basic components (diodes, transistors) is explained. In the second part, the fundamental building blocks of component manufacturing processes are presented.

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English tutorial course for students in the Master's 1 Physics program who are working toward professional proficiency in scientific English.

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This course is one of the cornerstones of modern physics. It provides a body of knowledge that is strictly necessary for all physics tracks, as it lays the groundwork for the theoretical description of the interaction between the electromagnetic field and elementary quantum systems such as two-level systems, atoms, and molecules. It also provides the knowledge necessary for understanding lasers, modern optical devices, and spectroscopic methods and analyses.

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The purpose of this module is to enable students to compare experimental results with their theoretical knowledge. Particular attention is given to writing up results and presenting them in the form of oral presentations. The work is organized into an eight-hour session for which the students choose a topic. They record their results and analyses in a lab notebook modeled after the protocols used in laboratories. At the end of the semester, students select a topic, which they develop into a final report that they defend orally. This course serves as preparation for the internships students will complete during their program.

Examples of available experiments: optical spectroscopy (IR, visible), gamma, X-ray, and acoustic spectroscopy; low-temperature photoluminescence; near-field spectroscopy (AFM, STM); electron microscopy...

The range of experiments offered covers the areas of physics taught in the various physics tracks. Students must choose from among these experiments those that best align with their interests. Significant effort is made to incorporate new data-acquisition technologies and the use of computer tools to compare experimental results with theory.

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Through two specific examples (X-ray diffraction and vibrations), this module shows in detail how the physical properties of a solid are modeled. The formalism will also be applied to finite systems, such as nanoparticles, and will remain valid for amorphous materials; however, special attention will be given to periodic systems (ranging from linear chains to protein crystals, including graphene and silicon). The concept of reciprocal lattice will naturally arise in connection with this periodicity.

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This course unit covers a review and in-depth exploration of programming techniques, as well as an introduction to computational physics. We will begin with a review of procedural programming using Python 3. We will then take an in-depth look at numerical methods relevant to physics, studying a selection of classical algorithms from numerical analysis and applying them to physics problems.

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This course is designed to introduce and develop several fundamental concepts and tools of non-relativistic quantum physics necessary for understanding the physical processes that describe the interactions between the elementary constituents of matter and radiation. We will also cover second quantization and the path integral formulation of quantum mechanics, which provide the ideal framework for the development of quantum field theory and its various applications (e.g., high-energy physics, condensed matter physics).

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Introduction to Advanced Statistical Physics: grand canonical ensemble; quantum statistics; quantum fluids (Bose-Einstein condensation, thermal radiation; Sommerfeld theory); phase transitions; Ising model; mean-field theory; dynamics of complex systems.

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The EU course “Condensed Matter Physics 2: Electronic Properties” is intended for students interested in solid-state physics.

Following on from the course unit “Condensed Matter Physics 1: Structural Properties,” this course unit covers the properties of electrons in crystalline solids, the band structure of electronic energy levels, and the basic concepts of semiconductor physics.

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Internship supervised by a faculty member/researcher in the field of nanophysics and quantum physics.

Dates: May–June

Duration: At least 7 weeks, extendable in July

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Knowing how to collect and process data are essential skills in a scientific and/or technical professional setting. The objective of this course is to address, as effectively as possible, three types of standard professional skills:

· Advanced use of spreadsheets and graphing software (MS Excel, LO-CALC) for scientific and technical purposes

· Network interconnections: infrastructure, the TCP/IP protocol suite, security

· Introduction to relational databases (MS Access, LO-BASE) – concepts and terminology, creating queries, graphical reports, forms.

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Mathematics for Computational Physics. Introduction to tools for the study of partial differential equations (distributions, variational formulation, Sobolev spaces).

Introduction to integral methods and their numerical implementation. Applications to diffraction problems in the harmonic regime.

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This course is designed to provide students with skills in the numerical solution of the Schrödinger equation in order to simulate complex quantum well structures. The course begins with a study of cases where the solution is analytical, followed by cases where the solution is semi-analytical, before moving on to the finite difference (FD) method. Various FD schemes are presented, each accompanied by an evaluation of convergence as a function of key parameters (domain truncation, number of samples, etc.). Finally, examples of concrete physical applications are examined.    

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This lecture unit presents the physical properties of various nanostructures, such as quantum wells, 1D photonic crystals, carbon nanotubes, and graphene. It covers their electronic (structure and transport), vibrational, and optical properties, as well as the radiation-matter interaction.

The goal will be to describe the development of low-dimensional materials and their associated electronic, photonic, and phononic structures, and to study transport phenomena, electron-photon and electron-phonon couplings, excitons, as well as the absorption, emission, and scattering of light.

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This course is an introduction to artificial intelligence for physicists. It aims to explore applications of deep learning using the TensorFlow and Keras libraries. It includes a presentation of examples of how deep learning is used in physics.

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English tutorial course for students in the Master 2 Physics program who are preparing for a career in an English-speaking professional environment in a contemporary context.

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This course unit covers the computer-based solution of electromagnetism problems. Using Maxwell’s equations, it demonstrates how to simulate the behavior of electromagnetic waves in various media. In particular, it includes a detailed implementation of simulations based on the finite difference time domain (FDTD) method.

An introduction to diffraction problems in the harmonic regime caused by a bounded obstacle will be provided for the case of scalar waves in 2D and 3D.

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This module aims to teach the operating principles of the main techniques used to characterize the structure (in volume and on the surface) and properties (optical, electronic, etc.) of condensed matter:

• X-ray and electron diffraction techniques
• optical spectroscopy techniques (absorption, reflection, luminescence)
• local probe microscopy

  This module aims to teach the operating principles of the main techniques used to characterize the structure (in volume and on the surface) and properties (optical, electronic, etc.) of condensed matter:

  • X-ray and electron diffraction techniques
  • optical spectroscopy techniques (absorption, reflection, luminescence)
  • local probe microscopy

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This course unit is specific to the NanoQuant track and provides high-level foundational training in the field of quantum technologies—that is, current and future developments in new technologies based on concepts such as quantum coherence and entanglement, which enable functionalities and sensitivities that surpass those of their classical counterparts.

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A laboratory internship lasting at least five months, supervised by a faculty member or researcher in the fields of nanophysics or quantum physics.

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This course is a hands-on training program in the main techniques of nanoscale characterization and nanotechnology:

• AFM
• SEM
• Photoluminescence
• X-ray diffraction
• Ellipsometry
• Optical Microscopy
• Source meter
• Capacitance Meter
• Manufacturing Processes for Microdevices in Cleanrooms

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This course aims to provide a foundation in astronomy and astrophysics, which will be useful in the other astrophysics courses in the master’s program. It also illustrates how concepts from physics are applied to describe astrophysical objects. Most of the concepts covered here will be explored in greater depth later in the^second-year courses.

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Fluids are all around us at all times and on every scale. Understanding fluid mechanics means understanding the mechanics of our surroundings—air and water, in particular. As such, hydrodynamics is part of a physicist’s basic knowledge.

The course “Hydrodynamics” provides an introduction to the mechanics of ideal incompressible fluids (Euler) and Newtonian viscous fluids (Navier-Stokes). Classical flow patterns are presented, along with the concepts of the boundary layer, instability, and turbulence. The focus is on physical concepts rather than on advanced mathematical or numerical solution methods.

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English tutorial course for students in the Master's 1 Physics program who are working toward professional proficiency in scientific English.

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This course is one of the cornerstones of modern physics. It provides a body of knowledge that is strictly necessary for all physics tracks, as it lays the groundwork for the theoretical description of the interaction between the electromagnetic field and elementary quantum systems such as two-level systems, atoms, and molecules. It also provides the knowledge necessary for understanding lasers, modern optical devices, and spectroscopic methods and analyses.

View the full page

The purpose of this module is to enable students to compare experimental results with their theoretical knowledge. Particular attention is given to writing up results and presenting them in the form of oral presentations. The work is organized into an eight-hour session for which the students choose a topic. They record their results and analyses in a lab notebook modeled after the protocols used in laboratories. At the end of the semester, students select a topic, which they develop into a final report that they defend orally. This course serves as preparation for the internships students will complete during their program.

Examples of available experiments: optical spectroscopy (IR, visible), gamma, X-ray, and acoustic spectroscopy; low-temperature photoluminescence; near-field spectroscopy (AFM, STM); electron microscopy...

The range of experiments offered covers the areas of physics taught in the various physics tracks. Students must choose from among these experiments those that best align with their interests. Significant effort is made to incorporate new data-acquisition technologies and the use of computer tools to compare experimental results with theory.

View the full page

Through two specific examples (X-ray diffraction and vibrations), this module shows in detail how the physical properties of a solid are modeled. The formalism will also be applied to finite systems, such as nanoparticles, and will remain valid for amorphous materials; however, special attention will be given to periodic systems (ranging from linear chains to protein crystals, including graphene and silicon). The concept of reciprocal lattice will naturally arise in connection with this periodicity.

View the full page

This course is designed to introduce and develop several fundamental concepts and tools of non-relativistic quantum physics necessary for understanding the physical processes that describe the interactions between the elementary constituents of matter and radiation. We will also cover second quantization and the path integral formulation of quantum mechanics, which provide the ideal framework for the development of quantum field theory and its various applications (e.g., high-energy physics, condensed matter physics).

View the full page

Introduction to Advanced Statistical Physics: grand canonical ensemble; quantum statistics; quantum fluids (Bose-Einstein condensation, thermal radiation; Sommerfeld theory); phase transitions; Ising model; mean-field theory; dynamics of complex systems.

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The EU course “Condensed Matter Physics 2: Electronic Properties” is intended for students interested in solid-state physics.

Following on from the course unit “Condensed Matter Physics 1: Structural Properties,” this course unit covers the properties of electrons in crystalline solids, the band structure of electronic energy levels, and the basic concepts of semiconductor physics.

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• Educational Approach

Students practice by conducting experiments under exam conditions to apply their knowledge and experimental skills and develop effective communication skills.

• Key Topics Covered in the Training

The topics covered are taken directly from the list of physics experiments included in the current CAPES physics–chemistry admission exam syllabus (a list published annually in the Official Bulletin of the Ministry of National Education).

• Digital Space

Acquisition (via a computer interface) of physical data from an experiment (Orphy_Lab and Orphi_GTI cards, Caliens camera).

- Analysis of a physics problem (mechanics, electricity, thermodynamics, waves, electromagnetism, wave optics) using data analysis software (Regressi).

- Basic coding and algorithmics using Python (with the option to use offline editors, such as EduPython, or online editors, such as Jupyter). Displaying and analyzing experimental data.

Application to the solution of simple differential equations in physics.

• Connection to Other EU Countries

This module, which begins in Semester 3, revisits the material covered in the first year in the “Teaching Physics” course units.

Students also draw on teaching situations they encounter during their fieldwork, as well as the material covered in the course units “Didactic and Pedagogical Support for Fieldwork” (S1, S2, S3, and S4) and “Didactics, Epistemology, and History of Science” (S2).

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Fluids are all around us at all times and on every scale. Understanding fluid mechanics means understanding the mechanics of our surroundings—air and water, in particular. As such, hydrodynamics is part of a physicist’s basic knowledge.

The course “Hydrodynamics” provides an introduction to the mechanics of ideal incompressible fluids (Euler) and Newtonian viscous fluids (Navier-Stokes). Classical flow patterns are presented, along with the concepts of the boundary layer, instability, and turbulence. The focus is on physical concepts rather than on advanced mathematical or numerical solution methods.

View the full page

English tutorial course for students in the Master's 1 Physics program who are working toward professional proficiency in scientific English.

View the full page

This course is one of the cornerstones of modern physics. It provides a body of knowledge that is strictly necessary for all physics tracks, as it lays the groundwork for the theoretical description of the interaction between the electromagnetic field and elementary quantum systems such as two-level systems, atoms, and molecules. It also provides the knowledge necessary for understanding lasers, modern optical devices, and spectroscopic methods and analyses.

View the full page

The purpose of this module is to enable students to compare experimental results with their theoretical knowledge. Particular attention is given to writing up results and presenting them in the form of oral presentations. The work is organized into an eight-hour session for which the students choose a topic. They record their results and analyses in a lab notebook modeled after the protocols used in laboratories. At the end of the semester, students select a topic, which they develop into a final report that they defend orally. This course serves as preparation for the internships students will complete during their program.

Examples of available experiments: optical spectroscopy (IR, visible), gamma, X-ray, and acoustic spectroscopy; low-temperature photoluminescence; near-field spectroscopy (AFM, STM); electron microscopy...

The range of experiments offered covers the areas of physics taught in the various physics tracks. Students must choose from among these experiments those that best align with their interests. Significant effort is made to incorporate new data-acquisition technologies and the use of computer tools to compare experimental results with theory.

View the full page

Through two specific examples (X-ray diffraction and vibrations), this module shows in detail how the physical properties of a solid are modeled. The formalism will also be applied to finite systems, such as nanoparticles, and will remain valid for amorphous materials; however, special attention will be given to periodic systems (ranging from linear chains to protein crystals, including graphene and silicon). The concept of reciprocal lattice will naturally arise in connection with this periodicity.

View the full page

The course aims to provide a general introduction to cellular and molecular biology and to contextualize the use of modern physics—through its quantitative methods and approaches—to describe biological systems and their complexity, from the molecular scale to the cellular and tissue scales.

Another fundamental topic covered is the quantification of phenomena, their physical interpretation, and their physical-mathematical modeling. The course provides an introduction to the philosophy and the full range of topics in this master’s program, which focuses on the study of the physical principles underlying the organization and dynamics of living and complex matter.

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This course unit covers a review and in-depth exploration of programming techniques, as well as an introduction to computational physics. We will begin with a review of procedural programming using Python 3. We will then take an in-depth look at numerical methods relevant to physics, studying a selection of classical algorithms from numerical analysis and applying them to physics problems.

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Introduction to Advanced Statistical Physics: grand canonical ensemble; quantum statistics; quantum fluids (Bose-Einstein condensation, thermal radiation; Sommerfeld theory); phase transitions; Ising model; mean-field theory; dynamics of complex systems.

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Conducting a research project in an academic or industrial laboratory.

Dates: May–June

Duration: At least 7 weeks, extendable in July

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The mechanical and thermal properties of materials are central to many applications in the field of energy materials. Following an introduction to these various fields of application, this course unit aims to define the different concepts necessary for understanding both the mechanical and thermal properties of materials, focusing exclusively on “bulk” materials.

Hourly volumes*:

            CM: 11: 00 a.m.

            TD: 9: 00 a.m.

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This course introduces the concepts, fundamentals, and orders of magnitude in the physics and physical chemistry of interfaces that govern the mesoscopic scale of matter and ultimately determine the behavior and properties of everyday objects—such as soil, milk, cheese, paints, inks, cosmetics, adhesives, lubricants, and many other technological processes—as well as biological cells and membranes.

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Knowing how to collect and process data are essential skills in a scientific and/or technical professional setting. The objective of this course is to address, as effectively as possible, three types of standard professional skills:

· Advanced use of spreadsheets and graphing software (MS Excel, LO-CALC) for scientific and technical purposes

· Network interconnections: infrastructure, the TCP/IP protocol suite, security

· Introduction to relational databases (MS Access, LO-BASE) – concepts and terminology, creating queries, graphical reports, forms.

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One of the major challenges associated with the use of various materials in our daily lives is their durability—and, consequently, their degradation. In this course, we will address issues related to material durability (resources, reserves, material criticality, etc.) as well as methodologies for studying durability (types of surface/volume aging, temporal extrapolation, multiscale analysis, combination of effects, experimental representation, and industrial validation). This will then enable us to model the kinetics of aging using various models.

The various types of degradation affecting polymers will then be analyzed.

Finally, the aging of various types of materials will be illustrated through a number of real-world case studies (concrete, ceramics, metals, and elastomers).

Hours per week*: 11 hours CM:

                                    9:00 a.m. Tutorial

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Polymer physics—to which this course serves as an introduction—focuses on the physical properties of covalently bonded chain-like assemblies ranging from a few dozen to a few million elementary molecules: polymers or macromolecules.

These synthetic or natural molecules can be observed in the solid state, liquid state, in solution, in a colloidal state, or confined to an interface.

Their highly distinctive physical properties have led to the development of specific theoretical tools and the emergence of this new branch of physics with numerous applications.

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A literature review on a research topic related to the program and potentially connected to the topic of the Master’s 2 internship.

80 hours of independent study spread out over the first semester of the M2 program. Several project progress meetings will be scheduled with the expert advisors and the program’s scientific coordinators.

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English tutorial course for students in the Master 2 Physics program who are preparing for a career in an English-speaking professional environment in a contemporary context.

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This module gives students the opportunity to learn about the unique aspects of the professional world and to prepare to enter it under the best possible conditions, particularly through sharing experiences with professionals in the field. Students practice successfully completing the job application process in a systematic manner by thoroughly analyzing job postings, crafting targeted resumes and cover letters, and preparing for job interviews (through role-playing and simulations).

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This course provides a general introduction to 1) the physics and mechanics of granular media and 2) their modeling using discrete methods (DEM). The multiscale nature of a granular material is discussed, ranging from the microscopic scale (contact interactions) to the macroscopic scale (structural scale). A phenomenological description of macroscopic behavior as well as microscopic properties is discussed for the static, quasi-static, and flow states of granular media. Micromechanical models and scale-change approaches based on dimensionless analyses, averaged quantities, stress transmission, and the presence of anisotropies are introduced. The influence of particle properties and contact interactions on the microstructure is also discussed. Numerical approaches such as discrete methods (Discrete Element Methods, DEM), regular methods (Molecular Dynamics), and non-regular methods (Contact Dynamics) are presented. In particular, the Contact Dynamics method will be applied to simple examples using the LMGC90 computational code.

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This module aims to teach the operating principles of the main techniques used to characterize the structure (in volume and on the surface) and properties (optical, electronic, etc.) of condensed matter:

• X-ray and electron diffraction techniques
• optical spectroscopy techniques (absorption, reflection, luminescence)
• local probe microscopy

  This module aims to teach the operating principles of the main techniques used to characterize the structure (in volume and on the surface) and properties (optical, electronic, etc.) of condensed matter:

  • X-ray and electron diffraction techniques
  • optical spectroscopy techniques (absorption, reflection, luminescence)
  • local probe microscopy

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This course unit provides an introduction to the field of complex fluids and active matter, with applications in both the physical chemistry of soft matter and the physics of living systems and biological objects.

It is common to both the PhyMV and SoftMat tracks.

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Conducting a long-term research project (6 months) at an academic or industrial research laboratory.

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The first part of this course covers additional topics in probability theory: conditional expectation and Gaussian vectors. The second part introduces one of the main families of discrete-time stochastic processes: Markov chains. These are sequences of dependent random variables, whose dependency relationship is relatively simple since each variable depends only on the previous one. They are also a very powerful modeling tool. We will study the main properties of these processes, as well as their long-run behavior and the estimation of their parameters.

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Fluids are all around us at all times and on every scale. Understanding fluid mechanics means understanding the mechanics of our surroundings—air and water, in particular. As such, hydrodynamics is part of a physicist’s basic knowledge.

The course “Hydrodynamics” provides an introduction to the mechanics of ideal incompressible fluids (Euler) and Newtonian viscous fluids (Navier-Stokes). Classical flow patterns are presented, along with the concepts of the boundary layer, instability, and turbulence. The focus is on physical concepts rather than on advanced mathematical or numerical solution methods.

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The course aims to provide a general introduction to cellular and molecular biology and to contextualize the use of modern physics—through its quantitative methods and approaches—to describe biological systems and their complexity, from the molecular scale to the cellular and tissue scales.

Another fundamental topic covered is the quantification of phenomena, their physical interpretation, and their physical-mathematical modeling. The course provides an introduction to the philosophy and the full range of topics in this master’s program, which focuses on the study of the physical principles underlying the organization and dynamics of living and complex matter.

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Introduction to Advanced Statistical Physics: grand canonical ensemble; quantum statistics; quantum fluids (Bose-Einstein condensation, thermal radiation; Sommerfeld theory); phase transitions; Ising model; mean-field theory; dynamics of complex systems.

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