Fisica | STATISTICAL MECHANICS

cod. 0522600016

STATISTICAL MECHANICS

	0522600016
	DIPARTIMENTO DI FISICA "E.R. CAIANIELLO"

	PHYSICS
	2013/2014

PERCORSO COMUNE

	YEAR OF COURSE 1
	YEAR OF DIDACTIC SYSTEM 2010
	SECONDO SEMESTRE

TEACHING UNITS

SSD	CFU	HOURS	ACTIVITY	TYPE OF ACTIVITY
FIS/02	4	32	LESSONS	SUPPLEMENTARY COMPULSORY SUBJECTS
FIS/02	2	24	EXERCISES	SUPPLEMENTARY COMPULSORY SUBJECTS

	Objectives
	TO EXTEND THE BASIC KNOWLEDGE OF STATISTICAL MECHANICS OF THE THREE YEARS DEGREE TO ADVANCED PROBLEMS AS QUANTUM SYSTEMS, INTERACTING SYSTEMS AND NON-EQUILIBRIUM SYSTEMS.

	Prerequisites
	GENERALITIES OF EQUILIBRIUM STATISTICAL MECHANICS. NON-INTERACTING CLASSICAL SYSTEMS (PERFECT GAS, PARAMAGNET ETC...) BASIC FORMALISM AND APPLICATIONS OF QUANTUM MECHANICS (WAVE FUNCTION, SCHROEDINGER EQUATION, QUANTUM PARTICLES IN A BOX, SPIN).

	Contents
	QUANTUM STATISTICAL MECHANICS. FUNDAMENTAL POSTULATES AND DENSITY MATRIX. LIOUVILLE EQUATION. MICROCANONICAL, CANONICAL AND GRAN CANONICAL ENSEMBLES. PARAMAGNETISM. PARTITION FUNCTION OF NON-INTERACTING PARTICLES. CLASSICAL DESCRIPTION OF QUANTUM PARTICLES. STATISTICS OF NON-INTERACTING PARTICLES. BOSONS. PHOTONS. FERMIONS. PHONONS. CLASSICAL LIMIT. BOSE-EINSTEIN CONDENSATION. LOW-TEMPERATURE PROPERTIES OF ELECTRONS IN METALS. INTERACTING SYSTEMS. PHASE TRANSITIONS. VAN DER WAALS THEORY. FERRO-PARAMAGNETIC TRANSITION. CRITICAL EXPONENTS. PERCOLATION. ISING MODEL. OTHER SYSTEMS DESCRIBED BY THE ISING MODEL: GAS-LATTICE, BINARY MIXTURES, ANTIFERROMAGNETS ETC... SPONTANEOUS SYMMETRY BREAKING. FLUCTUATION-DISSIPATION THEOREM (STATIC). MEAN-FIELD THEORIES (LANDAU, WEISS, BRAGG-WILLIAMS, VAN DER WAALS). CORRELATION FUNCTIONS. ORNSTEIN-ZERNIKE THEORY. LIMIT OF VALIDITY OF MEAN FIELD: GINZBURG CRITERION. EXACTLY SOLUBLE MODELS: 1D ISING MODEL, SPHERICAL MODEL. SCALING THEORY. UNIVERSALITY. BLOCK TRANSFORMATIONS AND RENORMALIZATION GROUP. DYNAMICS. HYDRODYNAMIC APPROACH. LANGEVIN EQUATION. FLUCTUATION-DISSIPATION THEOREM (TIME DEPENDENT). MASTER EQUATION. FOKKER-PLANCK EQUATION. BROWNIAN OSCILLATOR. BOLTZMANN EQUATION. H-THEOREM. SPECTRAL ANALYSIS AND THE WIENER-KINTCHIN THEOREM. FLUCTUATION THEOREMS.

QUANTUM STATISTICAL MECHANICS.

FUNDAMENTAL POSTULATES AND DENSITY MATRIX. LIOUVILLE EQUATION. MICROCANONICAL, CANONICAL AND GRAN CANONICAL ENSEMBLES. PARAMAGNETISM. PARTITION FUNCTION OF NON-INTERACTING PARTICLES. CLASSICAL DESCRIPTION OF QUANTUM PARTICLES.

STATISTICS OF NON-INTERACTING PARTICLES.

BOSONS. PHOTONS. FERMIONS. PHONONS. CLASSICAL LIMIT. BOSE-EINSTEIN CONDENSATION. LOW-TEMPERATURE PROPERTIES OF ELECTRONS IN METALS.

INTERACTING SYSTEMS.

PHASE TRANSITIONS. VAN DER WAALS THEORY. FERRO-PARAMAGNETIC TRANSITION. CRITICAL EXPONENTS. PERCOLATION. ISING MODEL. OTHER SYSTEMS DESCRIBED BY THE ISING MODEL: GAS-LATTICE, BINARY MIXTURES, ANTIFERROMAGNETS ETC... SPONTANEOUS SYMMETRY BREAKING. FLUCTUATION-DISSIPATION THEOREM (STATIC). MEAN-FIELD THEORIES (LANDAU, WEISS, BRAGG-WILLIAMS, VAN DER WAALS). CORRELATION FUNCTIONS. ORNSTEIN-ZERNIKE THEORY. LIMIT OF VALIDITY OF MEAN FIELD: GINZBURG CRITERION. EXACTLY SOLUBLE MODELS: 1D ISING MODEL, SPHERICAL MODEL. SCALING THEORY. UNIVERSALITY. BLOCK TRANSFORMATIONS AND RENORMALIZATION GROUP.

DYNAMICS.

HYDRODYNAMIC APPROACH. LANGEVIN EQUATION. FLUCTUATION-DISSIPATION THEOREM (TIME DEPENDENT). MASTER EQUATION. FOKKER-PLANCK EQUATION. BROWNIAN OSCILLATOR. BOLTZMANN EQUATION. H-THEOREM. SPECTRAL ANALYSIS AND THE WIENER-KINTCHIN THEOREM. FLUCTUATION THEOREMS.