PHYS-714 / 2 credits

Teacher: Aron Camille Didier Georges

Language: English


Only this year


This course introduces modern field-theoretical approaches to non-equilibrium systems. Through practical examples from quantum gases/optics, we construct the Keldysh formalism and explore the connections to classical stochastic field theory, hydrodynamics, and the dynamics of phase transitions.


Lecturer: Camille Aron

Please note that the first lecture will take place on February 28th, in room BSP 727, at 10 am.


Schwinger-Keldysh formalism
Time-dependent quantum mechanics
Keldysh path integral
Dissipative environment (Caldeira-Leggett)
Connection to Lindblad master equation

Non-equilibirum quantum fields
Interactions and perturbation theory
Noether, thermodynamics
Quantum kinetic equation


Stochastic field theory
Langevin and Fokker-Planck equations
Martin-Siggia-Rose-Janssen-De Dominicis path integral
Stochastic thermodynamics

Dynamics of phase transitions
Conservation laws, Hohenberg-Halperin classification
Driven-dissipative Bose-Einstein condensation
Gross-Pitaevskii equation
Connection to KPZ dynamics, Wilsonian RG


non-equilibrium; field theory; driven-dissipative dynamics; open quantum many-body systems; stochastic field theory; Schwinger-Keldysh formalism

Learning Prerequisites

Required courses

Prior knowledge of (second-quantized) quantum mechanics is required and very basic knowledge of field theory will be helpful (but not necessary)



Keldysh technique and non-linear sigma-model: basic principles and applications,
A. Kamenev, A. Levchenko, Advances in Physics 58, 197 (2009) & arXiv:0901.3586
Introduction to Nonequilibrium Statistical Mechanics with Quantum Field Theory
T Kita, Prog. Theor. Phys.123, 581 (2010) & arXiv:1005.0393

Ressources en bibliothèque

Moodle Link

In the programs

  • Exam form: Oral presentation (session free)
  • Subject examined: Introduction to field theory of driven-dissipative systems
  • Lecture: 28 Hour(s)
  • Type: optional

Reference week

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