Fisica | PHYSICS OF MANY BODY SYSTEMS

cod. 0522600007

PHYSICS OF MANY BODY SYSTEMS

	0522600007
	DEPARTMENT OF PHYSICS "E. R. CAIANIELLO"
	EQF7
	PHYSICS
	2022/2023

PERCORSO SHARED STUDY PATHWAY

	YEAR OF COURSE 2
	YEAR OF DIDACTIC SYSTEM 2021
	AUTUMN SEMESTER

TEACHING UNITS

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

EXAMS

	Exam	Date	Session
	APPELLO DI FEBBRAIO 2023	06/02/2023 - 10:00	SESSIONE ORDINARIA
	APPELLO DI FEBBRAIO 2023	06/02/2023 - 10:00	SESSIONE DI RECUPERO

	Objectives
	THE COURSE INTRODUCES THE STUDENTS TO 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 AND NON-EQUILIBRIUM PROPERTIES OF A WIDE RANGE OF MACROSCOPIC SYSTEMS. INCLUDING NEW PHENOMENA COMING FROM MANY-BODY INTERACTIONS, AS TOPOLOGICAL PHASES. 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 INTRODUCES THE STUDENTS TO 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 AND NON-EQUILIBRIUM PROPERTIES OF A WIDE RANGE OF MACROSCOPIC SYSTEMS.
INCLUDING NEW PHENOMENA COMING FROM MANY-BODY INTERACTIONS, AS TOPOLOGICAL PHASES.

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 THE POSTULATES AND OF THE BASIC NOTIONS IN: QUANTUM MECHANICS, CONDENSED MATTER THEORY, ELEMENTS OF 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. [6 H] LINEAR RESPONSE THEORY: GENERAL KUBO FORMULA AND ORIGIN OF RETARDED GREEN'S FUNCTION; KUBO FORMULA FOR CONDUCTIVITY; DIELECTRIC FUNCTION AND MAGNETIC SUSCEPTIBILITY. [4 H] 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. [8 H] MATSUBARA GREEN'S FUNCTION AND NON-EQUILIBRIUM GREEN'S FFUNCTION (KELDYSH); RELATION BETWEEN MATSUBARA AND TWO-TIME GREEN'S FUNCTION. [8 H] 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. [8 H] NON-EQUILIBRIUM (KELDYSH) GREEN'S FUNCTION. APPLICATIONS: CALCULATION OF CONDUCTANCE THORUGH A QUANTUM POINT CONTACT AND OTHER APPLICATIONS TO QUANTUM TRANSPORT THROUGH NANOSTRUCTURES[4H]; APPLICATIONS TO MODELS WITH INTERACTIONS: THE HUBBARD MODEL AND THE METAL-INSULATOR TRANSITION AND FERROMAGNETISM; MODELS WITH TOPOLOGICAL PHASES: THE KITAEV CHAIN AND THE SSH MODEL. .[8 H] INTRODUCTION TO OTHER METHODS FOR INTERACTING SYSTEMS. [2 H]

Contents

SECOND QUANTIZATION IN SOLID STATE PHYSICS: OCCUPATION NUMBER REPRESENTATION; CREATION AND ANNIHILATION OPERATORS; SYSTEMS WITH IDENTICAL PARTICLES; MODELS IN THE PARTICLE NUMBER REPRESENTATION. [6 H]
LINEAR RESPONSE THEORY: GENERAL KUBO FORMULA AND ORIGIN OF RETARDED GREEN'S FUNCTION; KUBO FORMULA FOR CONDUCTIVITY; DIELECTRIC FUNCTION AND MAGNETIC SUSCEPTIBILITY. [4 H]
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. [8 H]
MATSUBARA GREEN'S FUNCTION AND NON-EQUILIBRIUM GREEN'S FFUNCTION (KELDYSH); RELATION BETWEEN MATSUBARA AND TWO-TIME GREEN'S FUNCTION. [8 H]
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. [8 H]
NON-EQUILIBRIUM (KELDYSH) GREEN'S FUNCTION. APPLICATIONS: CALCULATION OF CONDUCTANCE THORUGH A QUANTUM POINT CONTACT AND OTHER APPLICATIONS TO QUANTUM TRANSPORT THROUGH NANOSTRUCTURES[4H];
APPLICATIONS TO MODELS WITH INTERACTIONS: THE HUBBARD MODEL AND THE METAL-INSULATOR TRANSITION AND FERROMAGNETISM; MODELS WITH TOPOLOGICAL PHASES: THE KITAEV CHAIN AND THE SSH MODEL. .[8 H]

INTRODUCTION TO OTHER METHODS FOR INTERACTING SYSTEMS. [2 H]

	Teaching Methods
	THE COURSE WILL BE CARRIED BY MEANS OF FRONTAL LECTURES AND SEMINARS. THE LECTURES WILL BE AIMED AT ILLUSTRATING METHODS FOR THE RESOLUTION OF HAMILTONIAN SYSTEMS WITH MANY PARTICLES AND IN THE PRESENCE OF INTERACTIONS. THE SEMINAR ACTIVITY WILL BE AIMED AT INTRODUCING STUDENTS INTO THE MOST RECENT TOPICS OF INTEREST FOR SCIENTIFIC RESEARCH IN THE FIELD OF MANY-BODY SYSTEMS, AS TOPOLOGICAL PHYSICS AND OUT OF EQUILIBRIUM SYSTEMS.

Teaching Methods

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

THE LECTURES WILL BE AIMED AT ILLUSTRATING METHODS FOR THE RESOLUTION OF HAMILTONIAN SYSTEMS WITH MANY PARTICLES AND IN THE PRESENCE OF INTERACTIONS. THE SEMINAR ACTIVITY WILL BE AIMED AT INTRODUCING STUDENTS INTO THE MOST RECENT TOPICS OF INTEREST FOR SCIENTIFIC RESEARCH IN THE FIELD OF MANY-BODY SYSTEMS, AS TOPOLOGICAL PHYSICS AND OUT OF EQUILIBRIUM SYSTEMS.

	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. THE MINIMUM VOTE (18) IS ATTRIBUTED TO THE STUDENT WHEN HE SHOWS UNCERTAINTIES IN THE FORMALISM AND RESOLUTION METHODS [EQUATIONS OF MOTIONS; GREEN'S FUNCTIONS] OF MANY-BODY HAMILTONIANS. THE MAXIMUM VOTE (30) IS ATTRIBUTED WHEN THE STUDENT SHOWS A DEEP KNOWLEDGE OF THE FORMALISM AND METHODS FOR THE STUDY OF MANY-BODY SYSTEMS; IS ABLE TO DISCUSS A RESEARCH ARTICLE AND SHOWS A NOTABLE CAPABILITY TO CONNECT TO THE VARIOUS APPROACHES TREATED DURING THE COURSE. THE MAXIMUM GRADE CUM LAUDE IS GIVEN WHEN THE STUDENT SHOWS A VERY DEEP KNOWLEDGE OF ALL THE THEORETICAL CONTENT AND TECHNICAL ASPECTS PRESENTED IN THE COURSE.

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.

THE MINIMUM VOTE (18) IS ATTRIBUTED TO THE STUDENT WHEN HE SHOWS UNCERTAINTIES IN THE FORMALISM AND RESOLUTION METHODS [EQUATIONS OF MOTIONS; GREEN'S FUNCTIONS] OF MANY-BODY HAMILTONIANS. THE MAXIMUM VOTE (30) IS ATTRIBUTED WHEN THE STUDENT SHOWS A DEEP KNOWLEDGE OF THE FORMALISM AND METHODS FOR THE STUDY OF MANY-BODY SYSTEMS; IS ABLE TO DISCUSS A RESEARCH ARTICLE AND SHOWS A NOTABLE CAPABILITY TO CONNECT TO THE VARIOUS APPROACHES TREATED DURING THE COURSE.
THE MAXIMUM GRADE CUM LAUDE IS GIVEN WHEN THE STUDENT SHOWS A VERY DEEP KNOWLEDGE OF ALL THE THEORETICAL CONTENT AND TECHNICAL ASPECTS PRESENTED IN THE COURSE.

	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) A.L. FETTER, J. D. WALECKA, QUANTUM MANY-PARTICLE PHYSICS, DOVER PUBLICATIONS (2003) ZAGOSKIN, QUANTUM THEORY OF MANY-BODY SYSTEMS, SPRINGER B. ANDREI BERNEVIG, TAYLOR L. HUGHES, TOPOLOGICAL INSULATORS AND TOPOLOGICAL SUPERCONDUCTORS, PRINCETON UNIVERSITY (2013)

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)
A.L. FETTER, J. D. WALECKA, QUANTUM MANY-PARTICLE PHYSICS, DOVER PUBLICATIONS (2003)
ZAGOSKIN, QUANTUM THEORY OF MANY-BODY SYSTEMS, SPRINGER
B. ANDREI BERNEVIG, TAYLOR L. HUGHES, TOPOLOGICAL INSULATORS AND TOPOLOGICAL SUPERCONDUCTORS, PRINCETON UNIVERSITY (2013)

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