Advanced statistical physics - Département de Physique de l'Ecole Normale supérieure

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Advanced statistical physics

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November 14 - 18, 2022 :
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Contact us - Student support and Graduate School office :
Tél : 01 44 32 35 60
enseignement@phys.ens.fr

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Next student seminar :
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Here you can find information about your internships:
Experimental Internship - Undergraduate program
Master ICFP first year Internship

News : ICFP Research seminars
November 14 - 18, 2022 :
All information about the program

Contact us - Student support and Graduate School office :
Tél : 01 44 32 35 60
enseignement@phys.ens.fr

Faculty : Christophe Texier (Prof PSud)

Tutor : Jean-Noël Aqua (MdC SU)
ECTS credits : 6

Language of instruction : English

Examination : Written exam

Description : Prerequisites :
equilibrium statistical physics (ensemble theory)

PART 1 : Out-of-equilibrium statistical physics

A. Introduction to stochastic processes
Langevin equation
Generalities on stochastic processes (Markov process,…)
Master equation (detailed balance,...)
Fokker-Planck equation
First passage and exit problem (application to Ahrrenius law,…)
Anomalous diffusion

B. Linear response theory
correlation functions and response functions
causality and Kramers-Kronig relation
Fluctuation-dissipation theorem
Onsager reciprocity relations
spatial structure of correlation functions

PART 2 : Introduction to phase transitions and critical phenomena

A. Generalities on phase transitions
First order and second order phase transitions
(ex: liquid-gas and the Ising model)
spontaneous symmetry breaking, ergodicity breaking

B. Mean field approach
Landau description
Ginzburg-Landau
spatial correlations
Fluctuations and the limit of the mean field approach (Ginzburg criterion)

C. Universality and scaling
scaling
critical exponents, anomalous dimensions
relations between exponents

D. Renormalisation group
example of the 1D Ising model
RG transformation
fixed points

E. Phase transition without symmetry breaking
topological phase transition : the XY model and the BKT transition

Quick links

Next student seminar :
Access to the program

Here you can find information about your internships:
Experimental Internship - Undergraduate program
Master ICFP first year Internship

News : ICFP Research seminars
November 14 - 18, 2022 :
All information about the program

Contact us - Student support and Graduate School office :
Tél : 01 44 32 35 60
enseignement@phys.ens.fr