This article reviews recent advances in the theory of the three-dimensional dilute
homogeneous Bose gas at zero and finite temperature. Effective-field-theory methods are …

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 …

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

The aim of this review is to introduce the reader to some of the physical notions and the
mathematical methods that are relevant to the study of nonlinear waves in Bose–Einstein …

We present a formal derivation of the mean-field expansion for dilute Bose–Einstein
condensates with two-particle interaction potentials which are weak and finite-range, but …

We study the dynamics of a vortex in an atomic Bose-condensed gas at finite temperature
within the Zaremba-Nikuni-Griffin formalism. In a harmonically trapped pancake-shaped …

We study the effects of quantum and thermal fluctuations on Bose-Bose mixtures at finite
temperature employing the time-dependent Hartree-Fock-Bogoliubov (TDHFB) theory. The …

We consider many-body effects on particle scattering in one-, two-, and three-dimensional
(3D) Bose gases. We show that at T= 0 these effects can be modeled by the simpler two …

We investigate the effects of quantum correlations on dipolar quantum droplets. To this end,
we derive self-consistent time-dependent Hartree-Fock-Bogoliubov equations that fairly …

We describe a number-conserving approach to the dynamics of Bose-Einstein condensed
dilute atomic gases. This builds upon the works of Gardiner [Phys. Rev. A 56, 1414 (1997)] …