Hot topics in cold gases : A mathematical physics perspective (Special Feature : The Takagi Lectures)

Gregor Wentzel, Sachindeo Vaidya

Jakob Yngvason

In these notes of six lectures on selected topics in the theory of cold, dilute Bose gases, presented at the 5th Warsaw School of Statistical Physics in June 2013, the following topics are discussed: 1) The concept of BEC, 2) the ground state energy of a dilute Bose gas with short range interactions, 3) Gross-Pitaevskii theory and BEC in trapped gases, 4) Bose gases in rotating traps and quantized vortices, and 5) strongly correlated phases in the lowest Landau level generated by rapid rotation.

Cristian V. Ciobanu

Robert Seiringer

We present an overview of mathematical results on the low temperature properties of dilute quantum gases, which have been obtained in the past few years. The presentation includes a discussion of Bose–Einstein condensation, the excitation spectrum for trapped gases and its relation to superfluidity, as well as the appearance of quantized vortices in rotating systems. All these properties are intensely being studied in current experiments on cold atomic gases. We will give a description of the mathematics involved in understanding these phenomena, starting from the underlying many-body Schrödinger equation.

Dimitri M. Gangardt

Jean-Paul Blaizot

These lectures introduce techniques that are used in the description of systems of particles and fields at high temperature (or density). These methods have a broad range of physical applications. We shall discuss two specific applications: one related to hot and dense matter composed of quarks and gluons, with temperatures in the tera Kelvin range, the other related to Bose-Einstein condensation in ultra-cold gases, with temperatures in the nano Kelvin range. As we shall see, in both systems, long wavelength collective phenomena lead to similar features, in spite of the huge difference in orders of magnitude of the respective energy scales.