This colloquium surveys a number of theoretical problems and open questions in the field of
two-dimensional dilute Bose gases with weak repulsive interactions. In contrast to three …

Basic properties of cold Bose atoms in optical lattices are reviewed. The main principles of
correct self-consistent description of arbitrary systems with Bose-Einstein condensate are …

We review recent developments in the physics of ultracold atomic and molecular gases in
optical lattices. Such systems are nearly perfect realisations of various kinds of Hubbard …

At zero temperature, a Galilean-invariant Bose fluid is expected to be fully superfluid. Here
we investigate theoretically and experimentally the quenching of the superfluid density of a …

This paper summarizes the experimental frontier of ultracold fermionic gases. It is based on
three lectures which one of the authors gave at the Varenna Summer School describing the …

An optical speckle potential is used to investigate the static and dynamic properties of a
Bose-Einstein condensate in the presence of disorder. With small levels of disorder, stripes …

We observe the suppression of the 1D transport of an interacting elongated Bose-Einstein
condensate in a random potential with an amplitude that is small compared to the typical …

The review is devoted to the elucidation of the basic problems arising in the theoretical
investigation of systems with Bose-Einstein condensate. Understanding these challenging …

The review deals with the physics of cold atomic gases in the presence of disorder. The
emphasis is on the theoretical developments, although several experiments are also briefly …

The achievement of Bose–Einstein condensation in ultra-cold vapours of alkali atoms has
given enormous impulse to the study of dilute atomic gases in condensed quantum states …