Japanese Journal of Mathematics

, Volume 8, Issue 2, pp 185-232

First online:

Hot topics in cold gases

A mathematical physics perspective
  • Robert SeiringerAffiliated withInstitute of Science and Technology (IST) Austria Email author 

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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.

Keywords and phrases

quantum statistical mechanics Bose–Einstein condensation dilute Bose gas superfluidity excitation spectrum

Mathematics Subject Classification (2010)

82B10 82-02 46N50