Fisica | PHYSICS OF MANY BODY SYSTEMS

cod. 0522600007

PHYSICS OF MANY BODY SYSTEMS

	0522600007
	DIPARTIMENTO DI FISICA "E.R. CAIANIELLO"

	PHYSICS
	2013/2014

PERCORSO COMUNE

	YEAR OF COURSE 2
	YEAR OF DIDACTIC SYSTEM 2010
	PRIMO SEMESTRE

TEACHING UNITS

	SSD	CFU	HOURS	ACTIVITY	TYPE OF ACTIVITY
	FIS/03	6	48	EXERCISES	SUPPLEMENTARY COMPULSORY SUBJECTS

	Objectives
	THE COURSE AIMS TO DELIVER TO THE STUDENTS ADVANCED RESEARCH METHODS IN CONDENSED MATTER. MOREOVER IT AIMS TO EXAMINE SOME PROBLEMS OF THE MANY BODY PHYSICS INVOLVING ALSO PHASE TRANSITIONS TO PUT IN EVIDENCE THE EFFICIENCY OF THE METHODS BY DEDUCING THERMODYNAMIC PROPERTIES OF A WIDE RANGE OF MACROSCOPIC SYSTEMS. ANOTHER OBJECTIVE IS TO RENDER THE STUDENTS ABLE TO READ SCIENTIFIC ARTICLES ON THE TOPIC.

THE COURSE AIMS TO DELIVER TO THE STUDENTS ADVANCED RESEARCH METHODS IN CONDENSED MATTER. MOREOVER IT AIMS TO EXAMINE SOME PROBLEMS OF THE MANY BODY PHYSICS INVOLVING ALSO PHASE TRANSITIONS TO PUT IN EVIDENCE THE EFFICIENCY OF THE METHODS BY DEDUCING THERMODYNAMIC PROPERTIES OF A WIDE RANGE OF MACROSCOPIC SYSTEMS. ANOTHER OBJECTIVE IS TO RENDER THE STUDENTS ABLE TO READ SCIENTIFIC ARTICLES ON THE TOPIC.

	Prerequisites
	THE COURSE ASSUMES THE KNOWLEDGE OF BASIC NOTIONS IN: QUANTUM MECHANICS, CONDENSED MATTER THEORY, SOLID STATE PHYSICS, STATISTICAL MECHANICS.

	Contents
	SECOND QUANTIZATION IN SOLID STATE PHYSICS: OCCUPATION NUMBER REPRESENTATION; CREATION AND ANNIHILATION OPERATORS; SYSTEMS WITH IDENTICAL PARTICLES; MODELS IN THE PARTICLE NUMBER REPRESENTATION. LINEAR RESPONSE THEORY: GENERAL KUBO FORMULA AND ORIGIN OF RETARDED GREEN'S FUNCTION; KUBO FORMULA FOR CONDUCTIVITY; DIELECTRIC FUNCTION AND MAGNETIC SUSCEPTIBILITY. TWO-TIME GREEN'S FUNCTION: RETARDED, ADVANCED AND CASUAL GREEN'S FUNCTION; SPECTRAL FUNCTION; KRAMER-KRONIG THEOREM AND FLUCTUATION-DISSIPATION THEOREM; EQUATION OF MOTION METHOD AND SPECTRAL DENSITY APPROACH. MATSUBARA GREEN'S FUNCTION AND NON-EQUILIBRIUM GREEN'S FFUNCTION (KELDYSH); RELATION BETWEEN MATSUBARA AND TWO-TIME GREEN'S FUNCTION. PERTURBATION THEORY AND FEYNMAN DIAGRAMS: PERTURBATIVE EXPANSION FOR THE DENSITY OPERATOR, FREE ENERGY AND GREEN'S FUNCTION; WICK'S THEOREM; FEYNMAN DIAGRAMS; DYSON'S EQUATION. APPLICATIONS: THE HUBBARD MODEL AND THE EQUATIONS OF MOTION APPROACH; INTERACTING BOSE GAS AND PERTURBATIVE EXPANSION; QUANTUM LIQUIDS.

Contents

SECOND QUANTIZATION IN SOLID STATE PHYSICS: OCCUPATION NUMBER REPRESENTATION; CREATION AND ANNIHILATION OPERATORS; SYSTEMS WITH IDENTICAL PARTICLES; MODELS IN THE PARTICLE NUMBER REPRESENTATION.
LINEAR RESPONSE THEORY: GENERAL KUBO FORMULA AND ORIGIN OF RETARDED GREEN'S FUNCTION; KUBO FORMULA FOR CONDUCTIVITY; DIELECTRIC FUNCTION AND MAGNETIC SUSCEPTIBILITY.
TWO-TIME GREEN'S FUNCTION: RETARDED, ADVANCED AND CASUAL GREEN'S FUNCTION; SPECTRAL FUNCTION; KRAMER-KRONIG THEOREM AND FLUCTUATION-DISSIPATION THEOREM;
EQUATION OF MOTION METHOD AND SPECTRAL DENSITY APPROACH.
MATSUBARA GREEN'S FUNCTION AND NON-EQUILIBRIUM GREEN'S FFUNCTION (KELDYSH); RELATION BETWEEN MATSUBARA AND TWO-TIME GREEN'S FUNCTION.
PERTURBATION THEORY AND FEYNMAN DIAGRAMS: PERTURBATIVE EXPANSION FOR THE DENSITY OPERATOR, FREE ENERGY AND GREEN'S FUNCTION; WICK'S THEOREM; FEYNMAN DIAGRAMS; DYSON'S EQUATION.
APPLICATIONS: THE HUBBARD MODEL AND THE EQUATIONS OF MOTION APPROACH; INTERACTING BOSE GAS AND PERTURBATIVE EXPANSION; QUANTUM LIQUIDS.

	Teaching Methods
	THE COURSE WILL BE CARRIED BY MEANS OF FRONTAL LECTURES.

	Verification of learning
	ORAL EXAMINATION AND DISCUSSION OF A TERM PAPER.

	Texts
	W. NOLTING, FUNDAMENTALS OF MANY BODY PHYSICS, SPRINGER (2009) J.W. NEGELE AND ORLAND, QUANTUM MANY-PARTICLE PHYSICS (1988) P. PHILLIP, ADVANCED SOLID STATE PHYSICS, (2003) D.G. MAHAN, MANY PARTICLE PHYSICS, DOVER (2000) D.N. ZUBAREV, NONEQUILIBRIUM STATISTICAL THERMODYNAMICS, NEW YORK, CONSULTANTS BUREAU (974)

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