The physics of one-dimensional interacting bosonic systems is reviewed. Beginning with
results from exactly solvable models and computational approaches, the concept of bosonic …

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 …

The mathematical study of the Bose gas goes back to the? rst quarter of the twentieth
century, with the invention of quantum mechanics. The name refers to the Indian physicist …

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 study the motion of a pointlike impurity in a Bose-Einstein condensate at T= 0. By solving
the Gross-Pitaevskii (GP) equation in a perturbative manner we calculate the induced mass …

We investigate the zero-temperature phase diagram of a gas of bosonic atoms in one-and
two-color standing-wave lattices in the framework of the Bose-Hubbard model. We first …

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 …

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 …

Recent 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 by Lieb and …