Hot Topics in Cold Gases

Abstract

Since the first experimental realization of Bose-Einstein condensation in cold atomic gases in 1995 there has been a surge of activity in this field. Ingenious experiments have allowed us to probe matter close to zero temperature and reveal some of the fascinating effects quantum mechanics has bestowed on nature. It is a challenge for mathematical physicists to understand these various phenomena from first principles, that is, starting from the underlying many-body Schrödinger equation. Recent progress in this direction concerns mainly equilibrium properties of dilute, cold quantum gases. We shall explain some of the results in this article, and describe the mathematics involved in understanding these phenomena. Topics include the ground state energy and the free energy at positive temperature, the effect of interparticle interaction on the critical temperature for Bose-Einstein condensation, as well as the occurrence of superfluidity and quantized vortices in rapidly rotating gases.

Plenary lecture given at the XVI International Congress on Mathematical Physics, Prague, August 3-8, 2009

References in corpus (5)

• Many-Body Physics with Ultracold Gases
• The ground state energy of the weakly interacting Bose gas at high density
• Strongly correlated phases in rapidly rotating Bose gases
• The Yrast Line of a Rapidly Rotating Bose Gas: Gross-Pitaevskii Regime
• Rigorous Upper Bound on the Critical Temperature of Dilute Bose Gases

Cited by in corpus (5)

• The excitation spectrum for weakly interacting bosons in a trap
• Concentration behavior of standing waves for almost mass critical nonlinear Schrödinger equations
• Some contributions to many-body quantum mathematics
• Scaling limits of bosonic ground states, from many-body to nonlinear Schr{ö}dinger
• Bose Gases at Positive Temperature and Non-Linear Gibbs Measures