M2 iCFP – Advanced statistical physics (Soft Matter track)

Lectures for the « Soft Matter & physics for biology » track of the Master 2 iCFP

Lectures : Christophe Texier (LPTMS, UPSay)

Tutorials : Jean-Noël Aqua (INSP, SU)

  • Lectures at ENS, room L378, 8h30-12h30
  • 13 weeks

Program

  • PART 1 : out-of-equilibrium statistical physics
    – Phenomenological description and stochastic processes (Langevin and Fokker-Planck approaches,…)
    – Linear response theory (correlation and response functions, fluctuation-dissipation,…)
  • PART 2 : phase transitions and critical phenomena
    – Mean field (Landau and Landau-Ginzburg approaches,…)
    – Fluctuations and the limits of mean field
    – Universality and scaling, renormalisation

Lecture notes

Lecture notes (update: 04/01/2022)

Tutorials

  • TD 1 : Langevin model and random processes
  • TD 2 :  Random processes
  • TD 3 : Correlations and fluctuations
  • TD 4 : Fokker-Planck approach
  • TD 5 : Random walks
  • TD 6 : FPE and SDE
  • TD 7 : Environment model and linear response
  • TD 8 : Phase transitions – mean field
  • TD 9 : Mean-field Debye-Hückel theory for charged fluids
  • TD 10 : Liquid crystals
  • TD 11 : Real space renormalization for the Ising model

tutorials (pdf)

Exams

Bibliography

For part 1:

  • D. Chandler, Introduction to modern statistical mechanics, Oxford, 1987
  • L. Landau & E. Lifshitz, Statistical physics, volume 5, Mir, 1966
  • M. Le Bellac, F. Mortessagne & G. Batrouni, Equilibrium and non-equilibrium statistical thermodynamnics, Cambridge, 2004
  • N. Pottier, Nonequilibrium statistical physics: linear irreversible processes, Oxford, 2009

on stochastic processes:

  • C. W. Gardiner, Handbook of stochastic methods for physics, chemistry and the natural sciences, Springer, 1989
  • H. Risken, The Fokker-Planck equation, Springer, 1989
  • N. G. van Kampen, Stochastic processes in physics and chemistry, North-Holland, 1992

For part 2:

an introduction (the beginning of the lectures)

  • C. Texier & G. Roux, Physique statistique, Dunod, 2017 → chapter 10

two synthetic books, very well written:

  • Edouard Brézin, Introduction to statistical field theory, Cambridge University Press
  • John  Cardy, Scaling and renormalization in statistical physics, Cambridge University Press

Two other excellent books:

  • R. K. Pathria & P. D. Beale, Statistical Physics, 3rd ed. Academic Press
  • Nigel Goldenfeld, Lectures on phase transitions and the renormalizationg group, ABP

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