# Many-Body Approaches to Quantum Fluids

PHYS-619 / **1 credit**

**Teacher: ** Invited lecturers (see below)

**Language:** English

**Remark:** Next time: Fall 2023

## Frequency

Only this year

## Summary

Starting from a microscopic description, the course introduces to the physics of quantum fluids focusing on basic concepts like Bose-Einstein condensation, superfluidity, and Fermi liquid theory.

## Content

oncentrating on quantum fluids as basic examples of quantum many body systems in condensed matter physics, I will give an introduction to the physics and phenomena arising due to the interplay of interaction and quantum statistics.

I will focus on the understanding from the microscopic point of view,

based on various theoretical tools from mean-field theory over diagramatic methods to variational and quantum Monte Carlo calculations.

Outline:

- Basics of statistical physics and quantum mechanics (some reminder)

- Dilute Bose gases: Mean-field treatments and beyond

- Macroscopic quantum effects: Bose-Einstein condensation and superfluidity

- Quasi-two-dimensional Bosons: Kosterlitz Thouless transition

- Normal Fermi liquids

- many-body wave functions

Computational methods and algorithms will be part of the practical work (TP).

## Note

Host: G. Carleo

## Keywords

Bose-Einstein condenstation, superfluidity, Kosterlitz-Thouless transition, Fermi liquid theory, electron gas, quantum Monte Carlo methods, diagramatic expansions

## Learning Prerequisites

## Required courses

Statistical physics

Quantum mechanics

basic scientific programming

## Resources

## Bibliography

Quantum Liquids by A.J. Leggett

Methods of Quantum Field Theory in Statistical Physics by A.A. Abrikosov, L.P. Gorkov, and I.E. Dzyaloshinski

Theory of Interacting Fermi Systems by P. Nozières

Interacting Electrons by R.M. Martin, L. Reining, and D.M. Ceperly

## Ressources en bibliothèque

- Quantum Liquids / Leggett
- Methods of Quantum Field Theory in Statistical Physics / Abrikosov
- Theory of Interacting Fermi Systems / Nozières
- Interacting Electrons / Martin

## Moodle Link

## In the programs

**Number of places:**20**Exam form:**Oral presentation (session free)**Subject examined:**Many-Body Approaches to Quantum Fluids**Lecture:**14 Hour(s)**Practical work:**4 Hour(s)