Quantum statistics and interactions

This course gives an introduction to the concepts of many-body quantum mechanics. We will describe the quantum statistics of bosons and fermions, and describe the quantum properties  of systems composed of many identical particles. The main theoretical ingredient for this purpose are the creation and annihilation operators of  quantum particles, in what is sometimes called the "second quantized formalism". 

We will study a selection of the topics listed below:
 
Chapter 1: Quantum statistics and theoretical tools in quantum mechanics
Density  operator.
Bosons, Fermions, quantum statistics.
Quantum states of identical particles.

Chapter 2: Bosons and light-matter interactions
Electromagnetic field quantization, field creation and annihilation operators
Fock states, coherent states
Jaynes-Cummings Hamiltonian and vacuum Rabi oscillations
Bose-Einstein condensation and Gross-Pitaevski equation

Chapter 3: Fermionic systems
Introduction to fermionic creation and annihilation operators
Fermi sea: electrons and holes
Hartree-Fock approximation
Hubbard model
Cooper pairs, Bogoliubov transformation
Published on June 5, 2021
Updated on September 5, 2022