"Dimensional reduction for cold Bose gases and the effects of a random
potential"
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Recent experimental advances in the field of cold trapped atoms allow to
investigate the properties of Bose gases in reduced geometries, e.g.
elongated or disk-shaped traps. In particular, experimental and
theoretical work has indicated conditions in which a trapped, low
density Bose gas ought to behave like the 1D delta-function Bose gas solved
years ago by Lieb and Liniger.
Important questions arise concerning the theoretical foundation of the
dimensional reduction, in particular as regards its derivation from the
full many-body Schrödinger equation for 3D bosons.
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The lecture will consist of two parts. I shall first give a brief survey
of the dimensional reduction of cold Bose gases in elongated or disk
shaped traps. In the second part I shall discuss the effects of a random
potential on the one-dimensional Lieb-Liniger model that emerges as a
limit of a three-dimensional gas in a suitable limit.