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 …

We review phase-space techniques based on the Wigner representation that provide an
approximate description of dilute ultra-cold Bose gases. In this approach the quantum field …

We study the truncated Wigner method applied to a weakly interacting spinless Bose-
condensed gas which is perturbed away from thermal equilibrium by a time-dependent …

The theoretical description of trapped weakly interacting Bose–Einstein condensates is
characterized by a large number of seemingly very different approaches which have been …

We provide a derivation of a more accurate version of the stochastic Gross–Pitaevskii
equation, as introduced by Gardiner et al (2002 J. Phys. B: At. Mol. Opt. Phys. 35 1555). This …

We show how to adapt the ideas of local energy and momentum conservation in order to
derive modifications to the Gross-Pitaevskii equation which can be used …

We develop a consistent perturbation theory in quantum fluctuations around the classical
evolution of a system of interacting bosons. The zero-order approximation gives the classical …

We propose a method to study the time evolution of Bose-Einstein condensed gases
perturbed from an initial thermal equilibrium, based on the Wigner representation of the N …

Analog models of gravity have been motivated by the possibility of investigating phenomena
not readily accessible in their cosmological counterparts. In this paper, we investigate the …

We extend the projected Gross-Pitaevskii equation formalism of Davis [Phys. Rev. Lett. 87,
160402 (2001)] to the experimentally relevant case of thermal Bose gases in harmonic …