Theory of statistical ensembles: density operators, postulates of statistical mechanics, quantum statistical ensembles, classical limit. Examples and applications. Phase transitions and critical phenomena: singularities in thermodynamic functions, Lee-Yang theory. Spontaneous symmetry breaking and ergodicity breaking. Mean field theory and Landau-Ginzburg theory. Universality, scale invariance, critical exponents. Renormalization group.
R. Balian, From microphysics to macrophysics (Springer)
N. Goldenfeld, Lectures on phase transitions and the renormalisation group (Perseus)
Learning Objectives
Acquired knowledge: The course is composed of two parts. In the first part there is an exposition of the fundamental concepts of equilibrium statistical mechanics, mainly focused on quantum and classical statistical ensembles.The second part of the course is devoted to phase transitions: after a phenomenological introduction, conceptual nodes are dealt with (thermodynamic singularities, breaking of symmetries and of ergodicity) followed by the theory of critical phenomena (mean field, Landau theory and Landau-Ginzburg theory, scale invariance and renormalization group).
Acquired competence: Mastering of conceptual bases of equilibrium statistical mechanics and of phase transitions theory. Solution of simple but nontrivial model in statistical mechanics.
Skills acquired (at the end of the course): Tools to understand more advanced monographs on statistical mechanics and phase transitions as well as of part of research literature.
Prerequisites
Analytical mechanics, basic quantum mechanics, and thermodynamics
Teaching Methods
6 CFU
Class hours: 48
extra material on the moodle platform
Further information
Office hours:
Wednesdays from 4:30 to 6:00 pm: or contact the teacher for other possibilities.
Coordinates: Dipartimento di Fisica e Astronomia, Polo Scientifico, Sesto Fiorentino, room 304 (2nd floor)
phone 0554572311 (int. 2311)
e-mail: lapo.casetti@unifi.it
Website: --
Type of Assessment
The final test is a traditional oral test. Nevertheless students who would like to may prepare a presentation of a subject, chosen together with the teacher, which contains an in-depth examination of one or more particular aspects of the course under a more general point of view. In this case, the first half of the exam will be the presentation and the discussion of the chosen subject, the second half will be a traditional oral test covering other aspects of the course.
Course program
Theory of statistical ensembles: density operators, postulates of statistical mechanics, quantum statistical ensembles, classical limit. Examples and applications. Theory of transformations between statistical ensembles. Phase transitions and critical phenomena: singularities in thermodynamic functions, Lee-Yang theory. Spontaneous symmetry breaking and ergodicity breaking. Mean field theory and Landau-Ginzburg theory. Universality, scale invariance, critical exponents. Renormalization group.