Statistical Mechanics

Basic course given by Giuseppe Santoro

Term: 1

Start: 01-10-2020 End: 18-12-2020 Room: 131 and on zoom

Credits: 6

Schedule: Mon 14:00 - 16:00, Wed 9:00 - 11:00

Program

The course, worth 6 credits and comprising 24 lectures (2h each), is organised into two main parts:

  1. Basic material
  2. Selected topics

The basic material contains pretty standard topics. Starting with a review of thermodynamics, the statistical ensembles are introduced, and standard applications (systems of free bosons and fermions) are illustrated. Next, after an interlude on transfer matrix and path-integral representation, the standard Weiss mean-field theory approach is presented, ending with a derivation of the Ginzburg-Landau action. 

The selected topics include, this year: a brief introduction to the transverse field quantum Ising chain, and two chapters on more modern topics related to the thermodynamics of small (quantum) non-equilibrium systems - the so-called stochastic thermodynamics - and the role of information and measurement in thermodynamics, starting from the Maxwell's demon, to the Landauer' principle, and so on.

A more detailed syllabus would be: 

Basic material:

  • Introduction to entropy and statistical mechanics
  • Review of thermodynamics
  • Statistical mechanics ensembles: microcanonical, canonical, and grandcanonical
  • Applications to free gases and waves.
    • Quantum statistical mechanics of harmonic oscillators, and of ideal Fermi and Bose gases.
    • Sommerfeld low-T expansion for Fermi systems; Bose-Einstein condensation.
  • Phase transitions, universality and critical phenomena (brief overview)
  • Transfer matrix method and quantum-classical correspondence
  • Mean Field Theory
  • Landau-Ginzburg action: from the Ising model to the φ4 field-theory

Selected topics:

  • A brief introduction to the quantum Ising chain in a transverse field (a more in dept treatment will be given in the hands-on course https://cm.sissa.it/phdsection/descriptioncourse.php?ID=23)
  • Stochastic thermodynamics: Clausius' and work inequalities and Jarzynski equality
  • The role of information and measurement in thermodynamics: Maxwell's demon, Szilard engine, Landauer's principle, and generalizations of Clausius' and work inequalities in presence of measurement and feedback/control

 

Online resources

Filename Size Date Modified
zoom_link.pdf 22.60 kB 2020-10-02 07:02:02
LNotes_SM.pdf 9.55 MB 2020-12-20 07:05:32