Physique statistique : Des concepts aux applications

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Retrouvez toutes les informations pour vos stages :
Stages L3
Stages M1 ICFP
Stages M2 ICFP

Actualités : Séminaire de Recherche ICFP
du 6 au 10 novembre 2017 :

Retrouvez le programme complet

Emploi du temps 2017-2018 :
Emploi du temps L3
Emploi du temps M1 ICFP
Emploi du temps M2 ICFP

Contact - Secrétariat de l’enseignement :
Tél : 01 44 32 35 61
enseignement@phys.ens.fr

Enseignant : Werner Krauth
Chargé des TD : Maurizio Fagotti et Olga Petrova
ECTS : 6
Langue d’enseignement : Anglais
Site web :

Description

Scope of the course
This lecture course on statistical mechanics will take students from the foundations of probability theory and statistical inference to the important models and the central concepts and techniques of statistical mechanics. The main focus will be on equilibrium and on classical systems, but we will also treat transport and dissipation, and discuss quantum statistical mechanics for Boson systems and quantum spin models.
Organization, grading
There will be 15 lectures and tutorial sessions, 8 graded homeworks (50% of the grade), and a written final exam (50%, also).
Planning
Lectures and tutorial sessions each Monday morning, from 4 September 2017 through 18 December 2017 (Lectures : 8:30 - 9:25 am, 9:35 - 10:30 am ; tutorials : 10:45 - 11:40 am, 11:50 am - 12:45 pm).

Final exam : 15 January 2018 8:30 - 12:30
Prerequisites
This course will be self-contained. Some prior exposure to elementary statistical or thermal physics on the undergraduate level may be useful.

Computing requirements

Probability, statistics, and statistical physics are today closely linked to computing. Students should be able to download, run and modify elementary Python programs. Many such programs will be provided, and some will have to be written for the homework sessions.

Syllabus

  1. Probability theory
    • Probabilities, probability distributions, sampling
    • Random variables
    • Expectations
    • Inequalities (Markov, Chebychev, Hoeffding)
    • Convergence of random variables (Laws of large numbers, CLT)
    • Lévy distributions
  2. Statistics (statistical inference, estimation, learning)
    • Point estimation, confidence intervals
    • Bootstrap
    • Method of moments
    • Maximum likelihood, Fisher information
    • Parametric Bootstrap
    • Bayes statistics
  3. Statistical mechanics and Thermodynamics
    • Rapid overview on the connection between statistical mechanics and thermodynamics
    • lightning review of ensembles and
    • lightning review of the main physical quantities (partition function, energy, free energy, entropy, chemical potential, correlation functions, etc).
  4. Physics in one dimension
    • One-dimensional hard spheres, virial expansion, partition function
    • One-dimensional Ising model
    • Transfer matrix
    • Kittel model
    •  Chui-Weeks model : Infinite-dimensional transfer matrix
    • One-dimensional Ising model with 1/r^2 interactions
  5. Two-dimensional Ising model : From Ising to Onsager
    • Peierls argument, Kramers-Wannier relation
    • Two-dimensional transfer matrix (following Schultz et al)
    • Jordan-Wigner transformation
    • Free energy calculation
    • Spontaneous magnetization, zero-field susceptibility
    • Kaufman, Ferdinand-Fisher, Beale
  6. Two-dimensional Ising model : From Kac and Ward to Saul and Kardar
    • Van der Waerden, low-temperature and high-temperature expansions
    • Duality
  7. Physics in two dimensions ( Kosterlitz-Thouless physics) : XY (planar rotor) model
    • Peierls argument
    •  Mermin-Wagner theorem
    • Non-universality
  8. Physics in two dimensions ( Kosterlitz-Thouless physics) : Particle systems, superfluids
  9. Physics in infinite dimensions : Mean-field theory, Scaling
  10. Physics in infinite dimensions : Landau theory
  11. Renormalization group
  12. The Solid state : Order parameters, correlation functions
  13. Quantum systems - bosons
  14. Quantum systems - spin systems
  15. Equilibrium and transport, Fluctuation-dissipation theorem.

References
Lecture notes will be available before each course.
Books

  1. L. Wasserman, "All of Statistics, A Concise Course in Statistical Inference" (Springer, 2005)
  2. W. Krauth, "Statistical Mechanics : Algorithms and Computations" (Oxford, 2006)
  3. M Plischke, B Bergersen, "Equilibrium Statistical Physics" (World Scientific)
  4. L. D. Landau, E. M. Lifshitz, "Statistical Physics" (Pergamon)

Accès rapides

Prochain Séminaire de la FIP :
Accéder au programme

Retrouvez toutes les informations pour vos stages :
Stages L3
Stages M1 ICFP
Stages M2 ICFP

Actualités : Séminaire de Recherche ICFP
du 6 au 10 novembre 2017 :

Retrouvez le programme complet

Emploi du temps 2017-2018 :
Emploi du temps L3
Emploi du temps M1 ICFP
Emploi du temps M2 ICFP

Contact - Secrétariat de l’enseignement :
Tél : 01 44 32 35 61
enseignement@phys.ens.fr