ADVANCED STATISTICAL MECHANICS

Anno accademico 2018/2019 - 1° anno - Curriculum ASTROPHYSICS, Curriculum CONDENSED MATTER PHYSICS, Curriculum NUCLEAR PHENOMENA AND THEIR APPLICATIONS e Curriculum THEORETICAL PHYSICS
Docente: Andrea RAPISARDA
Crediti: 6
SSD: FIS/02 - FISICA TEORICA, MODELLI E METODI MATEMATICI
Organizzazione didattica: 150 ore d'impegno totale, 100 di studio individuale, 35 di lezione frontale, 15 di laboratorio
Semestre:

Obiettivi formativi

The course aims at the understanding of the thermodynamic properties of macroscopic systems on the basis of statistical-dynamical behavior of their microscopic constituents.


Modalità di svolgimento dell'insegnamento

Lectures and excercises in the classroom


Prerequisiti richiesti

None


Frequenza lezioni

Compulsory


Contenuti del corso

Principles of Thermodynamics. Thermodynamic equilibrium. Thermodynamic Potentials. Kinetic Theory. H theorem of Boltzmann. Maxwell-Boltzmann distribution. Ensemble theory of Gibbs. Classical Statistical Mechanics: Phase space. Liouville's theorem. Principle of a priori equiprobability. Microcanonical ensemble. Virial theorem. Equipartition of energy. Classical ideal gas. Derivation of thermodynamics for almost isolated systems. Gibbs paradox. System in contact with a thermostat. Statistical concept of temperature. Canonical ensemble. Energy fluctuations. Systems with variable number of particles. Chemical potential. Grand-canonical ensemble. Fluctuations in density in open systems. Gibbs paradox and correct counting of microscopic states. Postulates of quantum statistical mechanics. Density matrix. Quantum Liouville equation. Formulation of the quantum theory of Gibbs ensemble. Third Law of Thermodynamics. Ideal gas of Fermi and Bose. Bose-Einstein condensation and superfluid systems. Electromagnetic excitations in a cavity. Thermal excitations in solids. Statistical equilibrium in white dwarf stars. Electron gas in metals. Low-temperature behavior of Bose and Fermi of a weakly imperfect gas. Elementary excitations in helium liquid. Classical interacting systems. Development cluster for a classic real gas. Development of the virial equation of state of a perfect gas. Derivation of Van der Waals forces. Phase transitions and critical phenomena. Critical indices and scale invariance. The Ising model for ferromagnetism and model of the lattice gas. The mean field theory. Renormalization group theory and its applications. Numerical Methods: The Monte Carlo method and molecular dynamics - Some algorithms and applications. Deterministic chaos and the foundations of statistical mechanics - Lyapunov Exponents - Kolmogorov-Sinai entropy. Stochastic processes.


Testi di riferimento

K. Huang : Statistical Mechanics, J. Wiley & Sons (1987)
R.K. Pathria : Statistical Mechanics, Pergamon Press (1996)
E. Ott: Chaos in Dynamical systems, Cambridge University Press (1993)



Programmazione del corso

 ArgomentiRiferimenti testi
1Thermodynamics K. Huang, Statistical Mechanics, J. Wiley & Sons (1987) 
2Ensembles theory K. Huang, Statistical Mechanics, J. Wiley & Sons (1987) 
3Phase transitions K. Huang, Statistical Mechanics, J. Wiley & Sons (1987); R.K. Pathria Statistical Mechanics, Pergamon Press (1996) 
4Critical PhenomenaK. Huang, Statistical Mechanics, J. Wiley & Sons (1987); R.K. Pathria Statistical Mechanics, Pergamon Press (1996) 
5Universality and Scaling K. Huang, Statistical Mechanics, J. Wiley & Sons (1987); R.K. Pathria Statistical Mechanics, Pergamon Press (1996) 
6Deterministic Chaos E. Ott: Chaos in Dynamical systems, Cambridge University Press (1993) 

Verifica dell'apprendimento

Modalità di verifica dell'apprendimento

Preparation of a short written dissertation on one of the topics of the programme for a general oral discussion on the main topics presented during the lectures


Esempi di domande e/o esercizi frequenti

Thermodynamic potentials

Ensemble equivalence

1st order and 2nd order Phase transitions

Bose-Einstein condensation

Solutions of the Ising model

Critical exponents