Japanese Journal of Mathematics

, Volume 8, Issue 2, pp 185–232

Hot topics in cold gases

A mathematical physics perspective

Authors

    • Institute of Science and Technology (IST) Austria
Article

DOI: 10.1007/s11537-013-1264-5

Cite this article as:
Seiringer, R. Jpn. J. Math. (2013) 8: 185. doi:10.1007/s11537-013-1264-5

Abstract

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 mechanicsBose–Einstein condensationdilute Bose gassuperfluidityexcitation spectrum

Mathematics Subject Classification (2010)

82B1082-0246N50

Copyright information

© The Mathematical Society of Japan and Springer Japan 2013