10771 - Multi-Particle Systems Theory

Learning outcomes

At the end of the course, the student knows the theoretical models necessary to deal with the study of many body systems. In particular, the student learns the techniques of second quantization and of functional integration for the analysis of interacting systems, with particular emphasis on the calculation of Green's functions with diagrammatic methods. The student is able to use theoretical techniques to describe the physical properties of a variety of strongly correlated systems; he/she can use both exact and approximation techniques for describing phase transitions.

Course contents

SEMESTER I (Teoria dei sistemi a molti corpi I)  

Introduction to many body theory: Reveiew of quantum mechanics, Identical particles, The formalism of second quantization, Review of quantum statistical mechanics, Quantum gases.

Functional integrals: Coherent states in quantum mechanics,  Coherent states for bosons, Coherent states for fermions, Feynman integral in quantum mechanics, Path integral for many body systems.

Green functions: Correlation functions: definitions and properties, Path integral and correlation functions, Perturbation theory.

SEMESTER II (Teoria dei sistemi a molti corpi II)  

Green functions and approximations: Dyson eqaution and Hartree-Fock approximation, Complements about functional integration.

Phase transitions: Ising model, General definitions and theory of phase transitions.

Superconductivity. Experimental description, Microscopic (BCS) description, Ginzburg-Landau theory for a superconductor; Applications, Vortices.

Ginzburg-Landau theory: Ising model, the O(N) model, the limits of the Ginzburg-Landau theory.

Readings/Bibliography

A.L. Fetter, J.D. Walecka, Quantum theory of Many-particle Systems.

G. Morandi,  F. Napoli, E. Ercolessi, Statistical Mechanics. An intermediate course.

R.P. Feynman, A.R. Hibbs, Quantum Mechanics and Path Integral

J.W. Negele, H. Orland, Quantum Many-Particle Systems

J.F. Annett, Superconductivity, Superfluids and Condensates 

G. Mussardo, Il modello di Ising. Introduzione alla Teoria dei Campi e delle Transizioni di Fase 

Teaching methods

Lectures in class

Assessment methods

Oral exam

Teaching tools

Lecture notes

Links to further information

http://www.df.unibo.it/fismat/theory/

Office hours

See the website of Elisa Ercolessi