Statistical Physics : Advanced and New applications - Département de Physique de l'Ecole Normale supérieure

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Statistical Physics : Advanced and New applications

Accès rapides

Prochain Séminaire de la FIP :
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Retrouvez toutes les informations pour vos stages :
Stages L3
Stages M1 ICFP

Actualités : Séminaire de Recherche ICFP
du 14 au 18 novembre 2022 :
Retrouvez le programme complet

Contact - Secrétariat de l’enseignement :
Tél : 01 44 32 35 60
enseignement@phys.ens.fr

Accès rapides

Prochain Séminaire de la FIP :
Accéder au programme

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

Actualités : Séminaire de Recherche ICFP
du 14 au 18 novembre 2022 :
Retrouvez le programme complet

Contact - Secrétariat de l’enseignement :
Tél : 01 44 32 35 60
enseignement@phys.ens.fr

Parcours Physique Theorique = cours obligatoire
Enseignant : Giulio Biroli
Chargé de TD : Gregory Schehr
ECTS : 6
Langue d’enseignement : Anglais
Site web :

Descriptif du cours

Statistical physics is witnessing a revolution : understanding the dynamics of a very large number of interactive
degrees of freedom, which has been from the beginning the main aim of statistical physics, has become now
a central problem in many fields such as physics, biology, computer science, just to cite a few.
Now more than ever, statistical physics is both for its methods and its applications a very powerful discipline
with a very broad range of theoretical methods and ramifications in many branches of science.

The aim of this series of lectures is facing the students with this very rich state of the art :
on one hand by teaching fundamental notions and methods of statistical physics and
at the same time by presenting its modern applications in physics and beyond.

The main topics of the lectures are :

Stochastic dynamics and thermal noise.

Field theory in statistical physics.

Stochastic thermodynamics, Time-Reversal symmetry, Fluctuation-Dissipation relations.

Selected topics in critical phenomena : The large dimensional limit (mean-field theory), the low dimensional limit (how long-range order is destroyed), basic notions of renormalization group, Finite Size Scaling.

Topological defects and phase transitions.

Dynamics and phase transitions.

Information Theory, computer science and statistical physics.

Equilibration and Thermalization.

Prerequisites

Concepts and techniques to be revised before the beginning of the first semester :

Equilibrium statistical physics : statistical ensembles, thermodynamics, basic notions of phase transitions.

Students should have a good knowledge of statistical ensembles (canonical, micro-canonical and grand-canonical)
and their use to compute thermodynamic properties of equilibrium systems.
Basic notions and examples of phase transitions are also required.

To have a concrete idea of the material requested, students can browse the
Kerson Huang’s book on "Statistical Mechanics" Chaps 1,2,6,7,8.
Students can use their favourite book to revise.
A non-exhaustive list of possible sources from which one can choose :
Physique Statistique, G. Roux et C. Texier
Physique Statistique, N. Pavloff at N. Sator
G. Montambaux, https://www.equipes.lps.u-psud.fr/Montambaux/polytechnique/PHY433/poly-PHY433-2017.pdf
Statistical Physics of Particles, M. Kardar
Statistical Mechanics, Order Parameters and Complexity, J. P. Sethna
Principles of condensed matter physics, P. Chaikin, T. Lubensky
Statistical Mechanics, K. Huang

Mathematical tools : basic probability theory, operator formalism.

A good working knowledge of basic probability theory will be important, in particular
probability measures, conditioned probability, averages and moments.
The basic working knowledge on operator formalism used for quantum mechanics
will be also required (functional operator, eigenstates, eigenvalues, etc).
The undergraduate texts the students had already used on these topics
will be enough to revise.

Documents joints

td1_msr_ou.pdf
(pdf - 170.1 ko)

td2_dna.pdf
(pdf - 508 ko)

td3.pdf
(pdf - 149.9 ko)

td4.pdf
(pdf - 227.2 ko)

td5_migdal_kadanoff.pdf
(pdf - 162.7 ko)

td6_nprg.pdf
(pdf - 192 ko)

td5_crystals.pdf
(pdf - 214 ko)

td8_xy_v2.pdf
(pdf - 223.2 ko)

references2.pdf
(pdf - 80.1 ko)

Accès rapides

Prochain Séminaire de la FIP :
Accéder au programme

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

Actualités : Séminaire de Recherche ICFP
du 14 au 18 novembre 2022 :
Retrouvez le programme complet

Contact - Secrétariat de l’enseignement :
Tél : 01 44 32 35 60
enseignement@phys.ens.fr