Advanced Statistical Physics and new Applications

Accès rapides

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 16 au 20 novembre 2020 :

Retrouvez le programme complet

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

Theoretical Physics = compulsory

Faculty : Giulio Biroli

Tutor : Gregory Schehr

ECTS credits : 6

Language of instruction : English

Examination:The grading will be based on two homeworks, one given at the end of October and one at the beginning of December. Both will count for 4/20 each. If students will be allowed back in class during the exam period then there will be a written exam, done in class, and without access to lecture notes. It will count for 12/20.

Covid-19 alternative examination : If students will not be allowed back in class during the exam period then the exam will be oral (maximum duration 45 mins) ; it will count for 12/20 : We will start by asking specific questions on the problem classes and the homeworks done during the year, and then ask questions on the course.


Web site :

 Description

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.

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 16 au 20 novembre 2020 :

Retrouvez le programme complet

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