Course code: PARTICLES, NUCLEI AND UNIVERSE (PNU) Semester 1 Contributes to: M1 General Physics Course director: Course teachers: Elias Khan (Institut de Physique Nucléaire) Grégory Moreau (Laboratoire de Physique Théorique), Laurent Verstraete (Institut d’Astrophysique Spatiale) Volume: Period: 40 hours lectures and 30 hours tutorials Weeks 37-50 8 ECTS (Major course) Assessment: Written partial and final examinations Language of tuition: English Course Objectives: Learn the basics features about the particle standard model, nuclear structure, nucleosynthesis, stellar evolution, and cosmology Course prerequisites and corequisites: -Classical mechanics -Basics in statistical physics, Quantum mechanics and Special relativity -Classical field theory: Maxwell equations This Major course constitutes preparatory lectures for the following Minor courses of the 2nd semester : «Astrophysics and Astroparticles», «Experiments and Applications in Sub-atomic Physics» and «General Relativity and Cosmology». Contents: This major covers six chapters, following the history of the synthesis of matter in the Universe: Chapter 1: Particles and symmetries (GM) Klein-Gordon equation & Time-dependent perturbation theory Application to processes with scalar particles Calculation of basic particle reactions / introducing the Feynman diagrams Symmetries of particles / reactions (spacetime, internal, gauge) Experiments: collisions, kinematics and conservation laws Chapter 2: Hadron synthesis (GM) The quark model The main hadron properties Experimental proofs: partons, colors and gluons Phenomenology of the hadrons Chapter 3: The primordial Universe (LV) I- The distant Universe: Objects and distances, distribution of matter - Evidence for dark matter - The cosmological principle - The expansion law and its recent acceleration - The FLRW metrics and the scale factor R(t) II- Cosmic evolution: The observational pillars for the Big Bang model - The energy content of the Universe, the critical density - The Friedmann equations - Applications III- The building of matter after big-bang Nucleosynthesis of light elements, the neutron-to-proton ratio, baryon density and baryon-to-photon ratio - The recombination, decoupling of matter and radiation Chapter 4: The nucleus, a unique manybody system (EK) Dimensionless study of many-body systems Finite systems, the spin-orbit rule The case of nuclei: from QCD to the nucleon-nucleon interaction, nuclear superfluidity From mean-field to magic numbers, the isospin symmetry, the nuclear chart
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Course code: PARTICLES, NUCLEI AND UNIVERSE (PNU) Semester 1Contributes to:
40 hours lectures and 30 hours tutorialsWeeks 37-50
8 ECTS (Major course)
Assessment: Written partial and final examinations
Language of tuition:
English
Course Objectives: Learn the basics features about the particle standard model, nuclear structure, nucleosynthesis, stellar evolution, and cosmology
Course prerequisites and corequisites: -Classical mechanics -Basics in statistical physics, Quantum mechanics and Special relativity-Classical field theory: Maxwell equations This Major course constitutes preparatory lectures for the following Minor courses of the 2ndsemester : «Astrophysics and Astroparticles», «Experiments and Applications in Sub-atomic Physics» and «General Relativity and Cosmology».
Contents:This major covers six chapters, following the history of the synthesis of matter in the Universe:
Chapter 1: Particles and symmetries (GM)Klein-Gordon equation & Time-dependent perturbation theory Application to processes with scalar particles Calculation of basic particle reactions / introducing the Feynman diagrams Symmetries of particles / reactions (spacetime, internal, gauge) Experiments: collisions, kinematics and conservation laws
Chapter 2: Hadron synthesis (GM)The quark model The main hadron properties Experimental proofs: partons, colors and gluons Phenomenology of the hadrons
Chapter 3: The primordial Universe (LV) I- The distant Universe: Objects and distances, distribution of matter - Evidence for dark matter - The cosmological principle - The expansion law and its recent acceleration - The FLRW metrics and the scale factor R(t) II- Cosmic evolution: The observational pillars for the Big Bang model - The energy content of the Universe, the critical density - The Friedmann equations - Applications III- The building of matter after big-bang Nucleosynthesis of light elements, the neutron-to-proton ratio, baryon density and baryon-to-photon ratio - The recombination, decoupling of matter and radiation
Chapter 4: The nucleus, a unique manybody system (EK)Dimensionless study of many-body systemsFinite systems, the spin-orbit ruleThe case of nuclei: from QCD to the nucleon-nucleon interaction, nuclear superfluidityFrom mean-field to magic numbers, the isospin symmetry, the nuclear chart
Chapter 5: From nuclear states to nuclear dynamics (EK)Nuclear states: localisation Nuclear spontaneous reactions: more than a dozen of radioactivitiesStatistical physics-like approaches: the liquid drop (mass parabola, the alpha radioactivity, fission and fusion)Probing nucleiAstronuclei
Chapter 6: Star formation and evolution (LV)I- From cloud to star: Gravitational instability, cloud fragmentation and Initial mass function - Free fall and hydrostatic evolution - Disk formation II- A star on the main sequence properties of a star on the main sequence, mass-luminosity relationship- Evolution in the HR diagram - Stellar nucleosynthesis - White dwarf stage
On completion of the course students should be able to:- Understand the major open questions in particle and nuclear physics, cosmology and stellar
evolution- Practice and predict basic physical related quantities: cross sections, star lifetime, particles
quantum numbers, etc.
Textbooks/bibliography:Quarks & leptons (Halzen, Martin)Gauge theory of elementary particle physics (Cheng, Li)Nuclear Physics in a Nutshell (C. Bertulani)Astrophysics in a nutshell (Maoz)The physics of stars (Phillips) Extragalactic astronomy and cosmology: an introduction (Schneider)
Course code: SOLID STATE PHYSICS (SSP) Semester 1
Contributes to:
M1 General Physics
Course director:Course teachers:
Philippe Mendels
Philippe Mendels, Agnes Barhélémy
Volume:Period:
40 hours lectures and 30 hours tutorialsWeeks 37-50
8 ECTS (Major course)
Assessment: Written partial and final examinations
Language of tuition:
English
Course Objectives: The aim of this course is to provide an introduction and a comprehensive view on modern solid state physics at an undergraduate level from the widespread basics to emergent fields of research which can be tackled at an elementary level (e.g. graphene). It emphasizes the fundamental aspects underlying quantum macroscopic phenomena in solids, which are present in most common materials of our daily life, metals, semiconductors, magnets. Each chapter will be illustrated by on-going research trends and/or applications (superconductivity, LEDs, magnetic memories,…)
Course prerequisites and corequisites: The prerequisites are usually taught at the level of the third year of university. In some cases, statistical Physics is not. See belowFundamentals of Quantum Mechanics. Book: Quantum Mechanics by C. Cohen-Tannoudi,
B. Diu, F. Laloë (vol. I and II), Ed WileyFundamentals of Statistical Physics. Book: Statistical Mechanics by K. Huang, Ed Wiley. Concepts of Statistical Physics needed for this course can be easily learnt in parallel.
Contents:
Chapter 1: Basic model of metals: the free electron gasGeneral introduction: the need for approximationsFree electron gas: why? Periodicity and screeningEnergy levels, density of states, B.V.K. boundary conditionsStatistical population: Fermi statistics, Fermi energy, specific heat, Pauli susceptibility,
comparison with the classical ideal gas and localized paramagnetismScanning tunneling microscopeQuantization of levels in a magnetic field: quantum oscillations
Chapter 2: Crystalline SolidsStructures: crystal lattice and primitive unit cell From 1 D to 3D: Bravais latticesDiffraction by crystalline solids and reciprocal latticeDiffraction in practice: lab. X-rays, synchrotron and neutron facilities, electronic microscopy: from formulas to hands on experimentsBeyond crystals: introduction to amorphous solids and soft matter
Chapter 3: Electronic structure of solidsElectrons in a periodic potential: Bloch’s theoremTight binding approach (1D, 2D), electronic instability: Peierls transitonThe physics of grapheneQuasi free electronsExperimental studies of band structures: photoemissionClassification of solids
Chapter 4: Dynamics of electronsBack to simple models: Drude approachBoltzmann equationDynamics of Bloch electrons: effective mass, holes
Chapter 5: Electrons at the nanoscaleCoulomb blockadeBand tailoring: heterostructures
Chapter 6: SemiconductorsGeneral introduction: Silicium, Germanium, III-V and II-VI familiesCarriers density: intrinsic semiconductorsHoles and electrons dynamics; conduction in an intrinsic semiconductorDoped semiconductorsTowards applications: diode, LED, solar cells, …
Chapter 7: MagnetismMacroscopic equations in magnetism and experimental set-ups: susceptibility, torque, high fieldsOrigins of magnetism in condensed matter: localized moments (from atoms to solids), delocalized electrons, diamagnetismParamagnetism of localized momentsInteracting moments: origin of the exchange interaction, Heisenberg Hamiltonian, Introduction to single molecule magnets Mean field treatment of interacting magnetic systems: ferro-, antiferro-, ferri- magnetismCollective excitations: spin waves; detection of spin waves: electronic resonance, neutron scatteringLocal probes of magnetismMagnetism and applications: domains, anisotropy, walls, magnets, modern tracks for magnetic recordingIntroduction to spintronics and its applications: novel non-volatile memories, non dissipative spin transistors, radiofrequency nano-oscillators
On completion of the course students should be able to:
- Attend any specialized course related to materials science, nano-condensed matter at the level of the second year of Master with a good theoretical background in solid state physics.
- Take more formal courses at the level of second year of Master covering advanced concepts used in Solid State Physics (M2 Fundamental Concepts in Physics) Have a strong background to follow GP year Minor Courses related to Condensed Matter Physics
Textbooks/bibliography:C. Kittel : Introduction to Solid State Physics (J. Wiley and Sons)N.W. Ashcroft and D.M. Mermin: Solid State Physics (Brooks and Cole)H. Alloul: Physics of Electrons in Solids (Springer)M.T. Dove : Structure and Dynamics (O.U.P)J. Singleton : Band theory and electronic properties of solids (O.U.P)S.J. Blundell : Magnetism in condensed matter (O.U.P)
Course code: ATOMS, MOLECULES and OPTICS (AMO) Semester 1Contributes to:
M1 General Physics
Course director:Course teachers:
Nicolas Dubreuil, Nouari Kebaili, Marc Hanna
Volume:Period:
40 hours lectures and 30 hours tutorialsWeeks 37-50
8 ECTS (Major course)
Assessment: Written final examination
Language of tuition:
English
Course Objectives: The physics of atoms and molecules, which constitutes the subject matter of this course rests on a long history of discoveries, both experimental and theoretical. Far from giving a complete account of the historical development, this introductory course aims to give an understanding of both theoretical foundations and key steps, which have occurred in this field. As a direct application of quantum mechanics it includes materials on basic atomic and molecular physics with discussion on structure, spectra and interaction with electric and magnetic field.
Course prerequisites and corequisites:
Contents:
Chapter 1: Introduction Key steps on electrons, photons and atoms studiesElements of quantum mechanicsOne-electron atoms:
Schrodinger equation for one-electron atomsSpecial hydrogenic systemsInteraction with electromagnetic radiationFine structure and hyperfine structureInteraction with external fields
Many-electron atoms:
Central field approximationThe periodic system of the elementsCorrections to the central field approximation : L-S and j-j couplingInteraction with electromagnetic radiation and with static fields
Molecular structure:The Born-Oppenheimer approximationMolecular orbital theoryThe calculation of electronic structureMolecular rotations and vibrationsMolecular electronic transitions
Chapter 2: Laser PhysicsAtoms and photons:
interaction processes, examples of absorption lines, effective area of a laser wave, populationrate equations.
Optical amplification:Intensity, influence of the origin of spectral broadening, index modulation in the amplifier.laser amplifiersThe oscillation condition, output intensity, case of the linear cavities, optical spectrum of thelaser oscillator.
Pulsed lasersPulsed oscillators and pulsed amplifiers
Laser opticsintuitive approach and detailed study of the spherical Gaussian wave, conditions for stablelaser cavities, higher order modes.
The different types of lasersLaser safetyApplications of lasers
Chapter 3: Nonlinear optics Introduction to non-linear opticsNonlinear Susceptibilities- Field notations- Nonlinear susceptibilities tensor: definition- Properties of the nonlinear susceptibilities - Contracted notation for the 2nd order nonlinear susceptibility- Spatial symmetriesNonlinear wave equation- Maxwell's equations- Propagation in a linear anisotropic material- Stationary nonlinear wave equation- Nonlinear wave equation in an isotropic materials- A physical picture: free and driven wavesSecond order nonlinearities- 2nd Harmonic generation-> Undepleted pump approximation regime->Phase matching considerations->Depleted pump regime- Frequency generation - Parametric processes ->optical parametric fluoresence and amplification->optical parametric oscillation : OPO- Quasi-phase matched materialsThird order nonlinearities- Four-wave Mixing
On completion of the course students should be able to:
Textbooks/bibliography:
Course code: ADVANCED STATISTICAL and QUANTUM MECHANICS(SQM)
Semester 2
Contributes to:
M1 General Physics
Course director:Course teachers:
Emmanuel TrizacEmmanuel Trizac, Grégory Moreau
Volume:Period:
40 hours lectures and 30 hours tutorialsWeeks 2 to 12
8 ECTS (Major course)
Assessment: Written partial and final examinations
Language of tuition:
English
Course Objectives: The Statistical Physics program provides an overview of the theory of phase transition, be they continuous or discontinuous. Mean-field approaches of the Landau family will be introduced, together with renormalization group techniques.
The aim of the second part of the course on Quantum Physics is to introduce the Quantum Field Theory for scalar fields - only coupled via a simple self-interaction - up to the calculation of basic scattering cross sections.
Course prerequisites and corequisites:
This course requires basic knowledge of probability theory (elementary laws generating functions, central limit theorem etc), Statistical Physics (see e.g. D. Chandler, Introduction to Modern Statistical Mechanics, or Diu et al, Physique Statistique), Quantum Mechanics (typically the content of the book « Quantum Mechanics » - Volume 1 & 2, by F. Laloë, B. Diu, C. Cohen-Tannoudji) and basic notions in Special Relativity (like the covariant formalism).
This Major course can be complemented by the Major course « Particles, Nuclei and the Universe » (1st semester) and of the Minor courses «Soft matter and biological physics », « Complex Systems and Information theory » , « Experiments and Applications in Sub-atomic Physics » (2nd semester).
Contents:
Chapter 1: Phase transitions and critical phenomena : qualitative approachesPhase transitions: problems raised and classification
Order parameter and symmetry breakingMagnetic models: Ising, Heisenberg, Potts and the likeLocal order and correlation functions
Chapter 2: Going quantitative From Weis molecular field to Landau approachesGinsburg Landau functionals
Chapter 3: Analytical Mechanics Principle of least action, Hamiltonian Euler-Lagrange equations Classical field theory Noether’s theorem
Chapter 4: Relativistic Quantum Framework Klein-Gordon equation Second quantization of a spin-0 field Green function for a free-field Canonical commutation relations
Chapter 5: Introduction to Quantum Field Theory Harmonic Oscillators Multi-particle states Evolution operator Simple scalar theory: — perturbation theory — scattering amplitudes
On completion of the course students should be: familiar with first order or continuous phase transitions, able to perform Ginzburg-Landau analysis, understand the rationale behind the renormalization group technique, apply the Noether’s theorem to any case, use path integral techniques, master advanced relativistic quantum mechanics, quantize spin-0 fields and ultimately calculate reaction amplitudes in Quantum Field Theory.
Textbooks/bibliography:From Microphysics to Macrophysics, R. Balian, Basic Concepts for Simple and Complex Liquids, J.-L.Barrat and J.-P. Hansen, Le Bellac, Peres, Landau-Lifshitz, Parisi, Messiah, Feynman, Pitaevski and Stringari, Klauber, Lahiri and Pal, Bailin and Love (first 75 pages), Peskin and Schroeder (first 100 pages).
Course code: NUCLEAR and PARTICLE PHYSICS (NP) Semester 2Contributes to:
30 hours lectures and 20 hours tutorialsWeeks 2-12
6 ECTS (Minor course)
Assessment: The final exam form can be either a writtensubject containing formal questions plus physics problem(s), or a research article tochoose, read and present orally (blackboard or slides).
Language of tuition:
English
Course Objectives: This Minor course proposes to explain general topics in Elementary Particle Physics. First the theoretical context necessary to describe spin-1/2 particles is presented in details, including notions of renormalisation. Then the Standard Model (SM) and its breaking of the ElectroWeak symmetry is introduced. A presentation follows on fermion masses and neutrino oscillations. From the experimental point of view, the course offers a description of important discoveries, at high-energy colliders, that have allowed historically to draw the present SM picture.
The Nuclear Physics part presents a general introduction on the atomic nucleus properties, then some of the basic models that can describe single particle and collective degrees of freedom of the nucleus, experimental techniques to investigate the properties of the nucleus and practical applications of Nuclear processes: material studies, diagnostics and therapeutics in Nuclear Medicine, radioactive dating.
Course prerequisites and corequisites: Those lectures require a solid background in Quantum Mechanics as well as basic notions in Special Relativity.This Minor course uses aspects developed within the Major course « Particles, Nuclei and the Universe » (1st semester) and it is complementary to the Major course « Advanced Statistical and Quantum Mechanics » (2nd semester).
Contents:
Chapter 1: Description of the atomic nucleus The nuclear landscape and basic facts for nuclear models; the deuteron properties Shell model and residual interaction - Independent particle model - Two particle configuration Collective excitations in even-even nuclei, vibrationel and rotational motion
Chapter 2: Experimental studies of the atomic nucleus Exciting the nucleus - Particle Accelerators - Reactions: direct and indirect reactions - Insight: production and separation of exotic nuclei Observing the nucleus - Radiation interaction with matter - Particle detection: general properties of radiat. detectors; semiconductor detectors Selected experimental techniques - Particle-gamma detection for nuclear structure studies - Life-time measurement techniques: from fast timing to beta decay
Chapter 3: Applications of nuclear physics (selected topics) Nuclear radioactivity and radioactive dating
Chapter 4: Fermionic Particles The Dirac Equation & Spinors Charge conjugation operator Lorentz transformations, Chirality Aspects of Renormalisation
Chapter 5: The Higgs Mechanism
Spontaneous breaking of global symmetry The Goldstone theorem : the U(1) example Mass generation for fermions, Yukawa couplings
Chapter 6: Experimental tests of the Standard Model Top quark observation at the Tevatron collider The Higgs scalar discovery at LHC
Chapter 7: Neutrinos
Their masses, oscillation experiments. Constraints from other experiments. Their nature: double beta decay processes.
On completion of the course students should be able to: write the Lagrangian of the ElectroWeak interactions, understand the Higgs boson mechanism for mass generation, have an overview of the Standard Model, describe the formalism of neutrino oscillations, calculate cross sections for reactions between spin-1/2 and spin-1 particles in Relativistic Quantum Theory, remember the strategies used in the most recent experimental discoveries of new particles at colliders, understand basic properties of the atomic nucleus through the models introduced in the lecture, have knowledge about different experimental techniques used to study the nucleus (excitation, detection) and possess a solid scientific background about fields of application of nuclear radioactivity.
Textbooks/bibliography:- Nuclear Structure from a Simple Perspective (Casten)- Introductory Nuclear Physics (Krane)- Introduction to Nuclear & Particle physics (Das, Ferbel)- Relativistic quantum mechanics (Klasen)- Quarks & leptons (Halzen, Martin)- Gauge theory of elementary particle physics (Cheng, Li)
Course code: ASTROPHYSICS and ASTROPARTICLES (AA) Semester 2Contributes to:
M1 General Physics
Course director:Course teachers:
Jonathan Biteau Jonathan Biteau, Bruno Maffei, Tiina Suomijärvi
Volume:Period:
30 hours lectures and 20 hours tutorialsWeeks 2 - 12
6 ECTS (Minor course)
Assessment: Case study and written final examination
Language of tuition:
English
Course Objectives: The course completes the program of the major course Particles, Nuclei and Universe on astrophysics by an introduction on our Galaxy, the interstellar matter, star formation and planetary systems. Basic knowledge on compact objects, large-scale structures and
magnetic fields are provided. Furthermore, the course introduces concepts related in particular to Astroparticle Physics: cosmic ray acceleration and propagation. An overview of various detection techniques of cosmic radiations and particles will be provided.
Course prerequisites and corequisites: The course requires knowledge of concepts introduced in the major course Particles, Nuclei and Universe.
Synchrotron self-Compton scenario Bremsstrahlung and the Heitler model Gamma-ray air showers
Chapter 4: Radiation processes - hadronic Pion production
muon, tau, and neutrino production Haronic air-showers and neutrino showers
Chapter 5: Large-scale structures, magnetic fields and observation methods Structures in the Universe and intergalactic magnetic field. Methods of observation across the EMspectrum, photometry, spectroscopy and interferometry.
Chapter 6: Cosmic-ray propagation Cosmic Ray Spectrum and Composition Interactions of Cosmic Rays with radiation fields (CMB, EBL) Propagation of charged particles in magnetic fields
Chapter 7: The interstellar medium Life cycle of the matter, composition (regions, elements, dust and grains) and processes of the ISM(radiation and dynamics), the tracers of matter.
Chapter 8: Stellar structure and evolution Stellar structure and equilibrium. Stellar evolution and terminal stages. White dwarfs, neutron stars,black holes and pulsars.
Chapter 9: Introduction to galaxies and our Galaxy The galaxy zoo, galaxy dynamics and structure. AGNs, radio galaxies and QUASARs. The Milkyway and its multi-wavelength observations.
Chapter 10: Planetary systems and extra-solar planets Solar system: planet properties, planet formation and evolution Exoplanets: interactions with their host stars, detection methods
On completion of the course students should be: familiar with the objects of the Universe, familiar with cosmic radiations and particles their production and propagation, have knowledge of their detection techniques.
Textbooks/bibliography:An introduction to Galaxies and Cosmology, Jones and Lambourne, Cam. Univ. PressExtrasolar Planets, P. Cassen, T. Guillot and A. Quirrenbach - Clayton, Principles of stellar evolution and nucleosynthesis, Chicago Press - Draine, physics of the interstellar and intergalactic medium, Princeton Series in Astrophysics- Particle Astrophysics, Donald Perkins, Oxford master series in Particle Physics, astrophysics andcosmology, Oxford University Press- High Energy Astrophysics, Malcolm S. Longair, vol. 1-3, Cambridge University Press
Course code: SOFT MATTER (SM) Semester 1Contributes to:
Assessment: Written partial and final examinations
Language of tuition:
English
Course Objectives: This course offers an introduction to soft condensed matter, or “complex fluids” with emphasis on physical principles that govern their behavior. Soft matter is a subfield of condensed matter comprising a variety of physical states that are easily deformed by thermal stresses or thermal fluctuations. They include liquids, colloids, polymers, foams, gels, granular materials, and a number of biological materials. These materials share an important common feature in that predominant physical behaviors occur at an energy scale comparable with room temperature thermal energy. Concepts, experimental techniques, andopen questions will be presented and discussed with students.
Course prerequisites and corequisites: Knowledge of thermodynamics and basic statistical mechanics and some familiarity with differential equations, hydrodynamics and phase diagrams.
Contents:
Chapter 1: Introduction What is soft matter? Forces, energies and timescales.
Chapter 2: Surface energy and interactionsSurface energy and tension Wetting: Young’s equation and contact anglesHydrophobicity and hydrophilicityCapillarity
Chapter 3: InteractionsVan der Waals interactions: from molecules to colloidal objectsElectrostatic interaction: linear approximation (Debye theory) Interactions between colloidal particles, DLVO potential.Stability and Aggregation Other interactions: Entropy-driven interactions, Hydrogen bounding Hydrophobic interactions
Chapter 4: Statistical Mechanics for Simple and Complex Liquids (Statics)Review of relevant results in Thermodynamics and Statistical Mechanics. Static structure of a liquid: radial distribution functions and structure factors. The hard-sphere model: thermodynamics, structure and melting. Phase diagram. Application to protein crystallization
Chapter 5: Elements of complex-fluid dynamics: Random walk and the diffusion equation. Brownian Motion of colloidal particles. Langevin Equation. Navier-Stokes equation and Reynolds number. Examples: Implications for living systems (Purcel’s “Life at low Reynold Nuber”)
Chapter 6: Self assemblyAggregation of amphiphilic molecules; Critical micelle concentration; Shape of micelles; Lipid bilayers, Nature of the cell membraneCurvature elasticity, Fluctuations of membranes Self assembly of colloidal systems Liquid crystalsExamples of self assembly: viruses Applications in nanotechnology
Chapter 7: Polymers and biological macromoleculesExamples of polymersSingle-chain statistics, self-avoiding walks Entropic forces and excluded volume Wormlike chain and persistence length, DNA Phase transitions: Flory Huggins free energy for solutions
Course Objectives: This set of lectures is devoted to an introduction to plasma physics and its applications: inparticular, thermonuclear fusion (ITER), space plasmas and plasma discharges, reactorsand thrusters.
Course prerequisites and corequisites: Basic knowledge (3rd year level) in classical electrodynamics, statistical physics, fluid mechanics, analytical mechanics and mathematical tools for physics. No major courses are requested to follow this course.
Contents:
Chapter 1: Basic plasma physicsCharacteristic length, velocity and time scales; Collective effects: electric and magnetic screenings; Elementary theory of transport, mobility and diffusion; Element of kinetic theory: Vlasov and Fokker-Planck equations; Wave and instability: ion acoustic wave, electron plasma wave.
Chapter 2: Advanced plasma physics From a kinetic to a fluid description; MHD equations: derivation and limits, Alfvén theoremand magnetic topology; Magnetic tension, Alfvén and magneto-acoustic waves; Magnetic reconnection: slow and fast, the MRI experiment and space applications; Static equilibrium: cylindrical case and the Grad-Shafranov equation for tokamaks.
Chapter 3: Applied plasma physics Discharge physics: high pressure, low pressure, breakdown criteria; Thermonuclear reactor and fusion physics; Introduction to capacitive, inductive and microwave reactors; Plasma thrusters and advanced applications.
On completion of the course students should be able to:Broad skills in theoretical and applied plasma physics with a broader interest in the field of plasma physics. Students should be able to follow in the best conditions the Master 2 in “Plasma Physics and Fusion”.
Course prerequisites and corequisites: Statistical physics and quantum mechanics
Contents:
- Concept of order parameter mean field theory of phase transitions- Non homogeneous systems, Ginzburg-Landau theory, functional derivative, domain walls, superconductivity.- Fluctuations, mean field correlations, Ginzburg criterion, Upper and lower critical dimension- Critical exponents, scaling and universality- Dynamics of phase transition, Time dependent Ginzburg-Landau, critical slowing down, Allen-Cahn and Cahn-Hilliard equations.- Mean-field for quantum systems, Gross-Pitaevkii equation
On completion of the course students should be able to:
Textbooks/bibliography:Principles of Condensed Matter Physics (P. M. Chaikin and T. C. Lubensky);
Phase Transitions and Collective Phenomena (B. Simons);
Course code: GENERAL RELATIVITY AND COSMOLOGY (GRC) Semester 2Contributes to: M1 General Physics
Course director:Course teachers:
Renaud Parentani, Bartjan van TentRenaud Parentani, Bartjan van Tent, Réza Ansari
Volume:Period:
30 hours lectures and 20 hours tutorialsWeeks 2 - 12
6 ECTS (Minor course)
Assessment: Written partial and final examination
Language of tuition:
English
Course Objectives:Part I: General Relativity
- Provide the basic concepts and tools to describe gravitational phenomena in terms of the
geometry of space-time.- Explain how the metric tensor and the principles of Relativity determine the trajectories of test particles.- Explain how the matter distribution determines the properties of the metric tensor.- Present the main predictions of General Relativity.
Part II: Primordial Cosmology- Provide a general overview of the history of the universe and introduce the basic concepts, definitions and equations of cosmology.- Explain in more detail the theory of some of the most important cosmological processes, in particular inflation, the production and evolution of cosmological fluctuations, and the cosmic microwave background radiation.- Present recent CMB observations, their results and implications for cosmology.
Part III: Observational Cosmology- Present an overview of the methodology of cosmological observations, especially optical observations.- Discuss the observational evidence for dark matter and dark energy.- Present recent results from optical surveys and future projects.
Course prerequisites and corequisites: This course is considered an introduction to the subject. As such it does not require much prior knowledge. It only requires basic notions of the Lagrangian formulation of classical mechanics, of Special Relativity, and of thermodynamics.No corequisites are necessary. It is nevertheless recommended to follow the Major "Particles, Nuclei and Universe", which contains several complementary notions. It is also recommended to follow the Major "Advanced Statistical and Quantum mechanics" to be ableto relate General Relativity to the theories of matter fields.
Contents:
Part I: General RelativityChapter 1: Equivalence principle, gravity and the geometry of space-time.Chapter 2: Propagation in curved space-times and geodesics.Chapter 3: Covariant derivatives, curvature tensor, Einstein's equations.Chapter 4: Predictions of General Relativity: bending of light, black holes, gravitational waves.
Part II: Primordial CosmologyChapter 5: Basics of cosmology; history and content of the universe.Chapter 6: Primordial inflation.Chapter 7: Theory of the generation and evolution of cosmological fluctuations during and after inflation; matter and gravitational wave power spectra.Chapter 8: Theory and observations of the cosmic microwave background radiation.
Part III: Observational CosmologyChapter 9: Hubble parameter measurements.Chapter 10: Dark matter.Chapter 11: Dark energy probes.
On completion of the course students should be able to:- Understand that gravitational phenomena, such as planetary orbits, Mercury's perihelion advance, the bending of light rays, gravitational collapse, and the cosmological expansion, should all be described in terms of the curvature of space-time. - Master the basic tools allowing us to describe these phenomena and to make predictions.- Understand how General Relativity relates to Special Relativity and the theory of Electromagnetism.- Have a good knowledge of the thermal history of the universe and the processes that play a role there, as well as the standard cosmological model and the observational evidence that supports it.- Be able to perform basic calculations in several areas of modern cosmology.- Be aware of the open questions and future experiments in cosmology.
Textbooks/bibliography:- J.B. Hartle, "Gravity, An Introduction to Einstein's General Relativity", Addison Wesley, 2003, ISBN 978-0805386622.
- B.Y. Schutz, "A First Course in General Relativity", Cambridge University Press, 2nd edition, 2009, ISBN 978-0521887052.- A.R. Liddle, "An Introduction to Modern Cosmology", Wiley, 2nd edition, 2003, ISBN 978-0470848357.- J. Rich, “Fundamentals of Cosmology”, Springer, 2010, ISBN 978-3-642-02800-7.- S. Dodelson, "Modern Cosmology", Academic Press, 2003, ISBN 978-0-12-219141-1.
Assessment: Written examination+ preparation of research papers
Language of tuition:
English
Course Objectives: Present some modern applications of quantum mechanics in macroscopic systems.
Course prerequisites and corequisites: The prerequisites are usually taught at the level of the third year of university.-Quantum mechanics (Fundamentals of Quantum Mechanics. Book : Quantum Mechanics by C. Cohen-Tannoudi,B. Diu, F. Laloë (vol. I and II), Ed WileyIn order to follow this course, this is strongly encouraged to also take in parallel the Major course in- Condensed Matter Physics
Contents:
Chapter 1: Superconductivity, superfluids and condensatesBose-Einstein Condensation and superfluidity Superconductivity: macroscopic aspects, microscopic theory, thermodynamics
Chapter 2: Mesoscopic physics and quantum transportQuantization of conductanceElectronic transport in mesoscopic systems (S-matrix formalism)Orbital magnetism and persistent currents in mesoscopic ringsJosephson effect
Chapter 3: Introduction to quantum informationQuantum Information: History, objectives, perspectivesQuantum bits and Bloch sphere
Entangled statesQuantum teleportation and EPR paradoxSimple examples of quantum computation
On completion of the course students should be able to:‐ Take more formal courses at the level of second year of Master covering advanced concepts used in Solid State Physics, Quantum physics, Nanoelectronics (M2 FundamentalConcepts in Physics, M2 Nano, etc.) -The student should be acquainted with the basics of superconductivity, superfluidity and quantum transport at the nanoscale. He will knows how quantum mechanics can help to transmit information in more secure way.
Textbooks/bibliography:- Principles of Condensed Matter Physics (P. M. Chaikin and T. C. Lubensky)- Superconductivity, Superfluids, and Condensates (J F Annett, Oxford Master Series in Condensed Matter Physics)- S. Datta, Quantum Transport: Atom to Transistor, Cambridge University Press, New York (2005)
- M. Le Bellac, A short introduction to Quantum information and quantum computation, Cambridge University Press
- M. A. Nielsen, and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge University press (2000)
Course code: Ne pas remplir
Sensors, Measurement and Signal Processing (SMS) Semester 1
Contributes to: M1 General Physics
Course director:Course teachers :
Réza ANSARI
Volume:Period:
25 hoursLectures : 5 x 2h = 10 h, Tutorials (TD) = 5 x 2h = 10 h , ComputerLab : 5 h
Course Objectives: Present the measurement process, the sources of uncertainties and the method to handle them. Basic signal processing technics and linear filterinf will aslo be presented .
Course prerequisites and corequisites: - basic knowledge of probabi lity ans statistics
- basic understanding of Fourier transform
- electrical circuits
SyllabusChap 1 : Sensors and measurements process - Metrology, physical quantities - Sensors : Principles of operations and general characteristics Chap 2 : Uncertainties and measurement errors - Statistical and systematic uncertainties, error propagation - Parameter estimationChap 3 : Signals in Fourier space - Fourier Transform and its properties - Convolution and auto-correlation, Spectral energy distribution - Fourier series, Sin/Cos TransformChap 4 : Linear Filtering & passive RLC filters - Linear time invariant systems, transfer function - Passive RLC filters - Bode diagramChap 5 : Digital Signal Processing - Windowing - Shannon Sampling theorem: sampling in time, sampling in frequency - DFT (Discrete Fourier Transform) and FFT
On completion of the course students should be able to:- Compute uncertainties when combining different measurements, how to control and decrease measurement errors- Undersatnd effect of filters used in measurement systems
- Use basic signal processing algorithms to extract information from time varying signals
1. Handbook of Modern Sensors - J. Fraden , Ed Springer / AIP press2. Les capteurs en instrumentation industrielle, G. Ash et al. , Ed. Dunod3. Digital Processing of Signals, Theory and Practice, 3rd ed. Maurice Bellanger, Wiley4. Méthodes et techniques du traitement du signal, Jacques Max, Jean-Louis Lacoume Ed. Dunod5. The Fourier Transform and its Applications, R.N. Bracewell, Mc Graw-Hill
Course code: MATHEMATICAL and STATISTICAL METHODS (MSM) Semester 1Contributes to:
M1 General Physics
Course director:Course teachers:
Pierre Désesquelles
Volume:Period:
30 hoursWeeks 37 - 50
3 ECTS
Assessment: Written final examination
Language of tuition:
English
Course Objectives: Learn the methods used to extract relevant information from experimental and simulated scientific data. Big data and Data mining.
Course prerequisites and corequisites: - basic knowledge of probability and statistics
- basic knowledge of matrix algebra, eigenvectors/values
Contents:
Chapter 1: Statistical toolsFrom probabilities to statisticsDistribution, pdf, distribution functionCharacterizationMatrix algebra
Chapter 2: Big dataWhat are big data and how to handle them?How to define information, clustering, discrimination?Multivariate analysis, characterization, discrimination, inference, decisionHow to extract information from random uncertainties, error propagation
Chapter 3: Cause/effect relationsCorrelation and cause/effectPartial correlationMultiple regression
Chapter 4: Evolving processesStates and transitionsAbsorbing processesRegular processes
On completion of the course students should be able to:- Manipulate scientific data and extract relevant information- Handle big data methods - Characterize the past and the future of evolving processes
Textbooks/bibliography:Data-Driven Modeling & Scientific Computation: Methods for Complex Systems & Big Data Paperback – September 15, 2013 by J. Nathan KutzMultivariate Data Analysis (7th Edition) by Joseph F. Hair Jr, William C. Black, Barry J. Babin and Rolph E. Anderson (Feb 23, 2009)
Course code: ADVANCED MATHEMATICS for PHYSICS (AMP) Semester 2Contributes to:
Course Objectives: To acquire familiarity and operational knowledge of the mathematics of symmetry groups, asa transversal and structuring notion of modern Physics, from condensed matter to particle physics.
Course prerequisites and corequisites: -Elementary quantum mechanics (Hilbert spaces, operators);-Elementary linear algebra (Vector spaces, matrices etc).
Contents:
Chapter 1: General Group theory (definitions and main theorems, important examples, compact topological groups and Haar integral)
Chapter 2: General aspects of the Representation Theory of Groups (operations on finite dimensionalrepresentations of compact groups, irreducible representations, complete reducibility, Schur's orthogonality relations, character theory, character tables for finite groups, projective representations in quantum mechanics)
Chapter 3: Some Finite Isometry groups (finite reflection groups, root systems, crystallographic root systems and Dynkin diagrams, 3d point groups)
Chapter 4: Introduction to Lie groups, Lie algebras and their representations (definition of Lie groups and their Lie algebras, root systems, Cartan's classification of simple complex Lie algebras, representations of Lie algebras and theory of weights, Weyl's character formula. Typical examples include SU(2) and SU(3) as relevant to Particle Physics and, if time permits, the Lorentz and Poincarégroups of Special Relativity).
On completion of the course students should be able to:-Handle the physically relevant mathematics of group theory and representation theory;-Manipulate the classical Lie groups and their representations;-Follow any advanced M2 lecture involving or relying on those notions.
Textbooks/bibliography:-Kosmann-Schwartzbach, Groups and symmetries;-Sternberg, Group theory and physics;-Fulton and Harris, Representation Theory.
Course code: EXPERIMENTAL PHYSICS Semester 1 - 2Contributes to:
M1 General Physics
Course director:Course teachers :
Carole Gaulard
Volume:Period:
50 hours 6 ECTS
Assessment: Written report
Language of tuition:
English
Course Objectives: To apply the knowledge learnt in the different courses to experimental physics. To work in different laboratories on complex and large experiments.
Course prerequisites and corequisites: To attend the corresponding courses
Contents:
LIST OF EXPERIMENTS Signal processing (IAS)
Radioactivity and cosmic radiations (IPN)- Gamma spectrometry
- Internal conversion
Condensed matter (Magistère bat 470)
-Magnetization measurements: from paramagnetism to superconductivity - Superconductivity: conductivity measurements, quantitative study of flux pinning, SQUID basics
On completion of the course students should be able to:
Textbooks/bibliography:- Glenn F. Knoll – Radiation Detection and Measurement- Syed Naeem Ahmed – Physics & Engineering of Radiation Detection
Course code: FRENCH COURSE (FLE) Semester 1 Contributes to:
M1 General Physics
Course director:Course teachers:
Roselyne Debrick
Volume: 25 hours 3 ECTS
Period: Assessment: Written examination
Language of tuition:
French
Course Objectives:
Provide basic knowledge of the French language.
Course prerequisites and corequisites: Students will be in different groups following their initial knowledge.
Contents:
On completion of the course students should be able to:
