Fisica | PHYSICS OF MANY BODY SYSTEMS

cod. 0522600007

PHYSICS OF MANY BODY SYSTEMS

	0522600007
	DIPARTIMENTO DI FISICA "E.R. CAIANIELLO"
	EQF7
	PHYSICS
	2016/2017

PERCORSO COMUNE Cohort 2015/2016

	YEAR OF COURSE 2
	YEAR OF DIDACTIC SYSTEM 2014
	PRIMO SEMESTRE

TEACHING UNITS

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

	Objectives
	THE COURSE AIMS TO PROVIDE TO THE STUDENTS ADVANCED RESEARCH METHODS IN CONDENSED MATTER PHYSICS AND LOW ENERGY THEORETICAL PHYSICS. KNOWLEDGE AND UNDERSTANDING: IT AIMS TO EXAMINE SOME PROBLEMS OF THE MANY BODY PHYSICS INVOLVING LINEAR RESPONSE THEORY AND PHASE TRANSITIONS TO PUT IN EVIDENCE THE EFFICIENCY OF THE METHODS (GREEN'S FUNCTION AND DIAGRAMMATIC TECHNIQUE) BY DEDUCING THERMODYNAMIC PROPERTIES OF A WIDE RANGE OF MACROSCOPIC SYSTEMS. APPLYING KNOWLEDGE AND UNDERSTANDING: ANOTHER OBJECTIVE IS TO RENDER THE STUDENTS ABLE TO READ SCIENTIFIC ARTICLES ON THE TOPIC AND APPLY THE METHODS TO MANY-PARTICLE SYSTEM HAMILTONIANS WITH EXTERNAL POTENTIALS AND INTERACTIONS.

THE COURSE AIMS TO PROVIDE TO THE STUDENTS ADVANCED RESEARCH METHODS IN CONDENSED MATTER PHYSICS AND LOW ENERGY THEORETICAL PHYSICS.

KNOWLEDGE AND UNDERSTANDING:
IT AIMS TO EXAMINE SOME PROBLEMS OF THE MANY BODY PHYSICS INVOLVING LINEAR RESPONSE THEORY AND PHASE TRANSITIONS TO PUT IN EVIDENCE THE EFFICIENCY OF THE METHODS (GREEN'S FUNCTION AND DIAGRAMMATIC TECHNIQUE) BY DEDUCING THERMODYNAMIC PROPERTIES OF A WIDE RANGE OF MACROSCOPIC SYSTEMS.

APPLYING KNOWLEDGE AND UNDERSTANDING:
ANOTHER OBJECTIVE IS TO RENDER THE STUDENTS ABLE TO READ SCIENTIFIC ARTICLES ON THE TOPIC AND APPLY THE METHODS TO MANY-PARTICLE SYSTEM HAMILTONIANS WITH EXTERNAL POTENTIALS AND INTERACTIONS.

	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 QUANTUM LIQUIDS. QUANTUM TRANSPORT THROUGH NANOSTRUCTURES (QUANTUM DOTS AND NANOWIRES)

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 QUANTUM LIQUIDS. QUANTUM TRANSPORT THROUGH NANOSTRUCTURES (QUANTUM DOTS AND NANOWIRES)

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

	Verification of learning
	ORAL EXAMINATION AND DISCUSSION OF A TERM PAPER TO VERIFY THE CAPACITY OF EXPOSING ON THE PHENOMENOLOGICAL AND TECHNICAL ASPECTS OF MANY-BODY MODELS.

	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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