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The phase transition to a Bose-Einstein condensate is unusual in that it is not necessarily driven by inter-particle interactions but can occur in an ideal gas as a result of a purely statistical saturation of excited states. However,…
We consider a Bose-Einstein condensate, which is confined in a very tight toroidal/annular trap, in the presence of a potential, which breaks the axial symmetry of the Hamiltonian. We investigate the stationary states of the condensate,…
In this paper we study nonequilibrium dynamics of one dimensional Bose gas from the general perspective of dynamics of integrable systems. After outlining and critically reviewing methods based on inverse scattering transform, intertwining…
The emergence of a non-equilibrium Bose-Einstein-like condensation of magnons in rf-pumped magnetic thin films has recently been experimentally observed. We present here a complete theoretical description of the non-equilibrium processes…
A self-consistent mean-field theory for bosons for T>0 is used to reconcile predictions of collapse with recent observations of Bose-Einstein condensation of 7Li. Eigenfunctions of a (non-separable) Hamiltonian that includes the anisotropic…
The dynamical evolution of a Bose-Einstein condensate trapped in a one-dimensional lattice potential is investigated theoretically in the framework of the Bose-Hubbard model. The emphasis is set on the far-from-equilibrium evolution in a…
We present a variational solution of the Langevin field equation describing the nonequilibrium dynamics of a harmonically trapped Bose-Einstein condensate. If the thermal cloud remains in equilibrium at all times, we find that the equation…
We present a kinetic description of Bose-Einstein condensation for particle systems being out of thermal equilibrium, which may happen for gluons produced in the early stage of ultra-relativistic heavy-ion collisions. The dynamics of bosons…
We prove two equilibrium properties of a system of interacting atoms in three or higher dimensional continuous space. (i) If the particles interact via pair potentials of a nonnegative Fourier transform, their self-organization into…
We consider the homogeneous Bose gas in the three-dimensional unit torus, where $N$ particles interact via a two-body potential of the form $N^{-1} v(x)$. The system is studied at inverse temperatures of order $N^{-2/3}$, which corresponds…
The interplay between spontaneously broken gauge symmetries and Bose-Einstein condensation has long been controversially discussed in science, since the equation of motions are invariant under phase transformations. Within the present model…
We investigate the thermodynamic behaviour of a Bose gas interacting with repulsive forces and confined in a harmonic anisotropic trap. We develop the formalism of mean field theory for non uniform systems at finite temperature, based on…
We study the bosonic Boltzmann-Nordheim kinetic equation, which describes the kinetic regime of weakly interacting bosons with s-wave scattering only. We consider a spatially homogeneous fluid with an isotropic momentum distribution. The…
We investigate the cyclotron dynamics of Bose-Einstein condensate (BEC) in a quadruple-well potential with synthetic gauge fields. We use laser-assisted tunneling to generate large tunable effective magnetic fields for BEC. The mean…
We consider the linear and nonlinear Schr\"odinger equation for a Bose-Einstein condensate in a harmonic trap with $\cal {PT}$-symmetric double-delta function loss and gain terms. We verify that the conditions for the applicability of a…
We report on the out-of-equilibrium dynamics of a Bose-Einstein condensate (BEC) placed in an optical lattice whose phase is suddenly modulated. The frequency and the amplitude of modulation are chosen to ensure a negative renormalized…
The compact groups such as $SU(n)$ and $SO(n)$ groups have been heavily studied and applied in the study of quantum many body systems. However, the non-compact groups such as the real symplectic groups are less touched. In this paper, we…
There is a wide-spread belief in the literature on Bose-Einstein condensation of interacting atoms that all variants of mean-field theory incorrectly describe the condensation phase transition, exhibiting, instead of the necessary…
We study a two component Bose-Einstein condensate in the presence of an inhomogeneous artificial gauge field. In response to this field, the condensate forms a localised vortex lattice structure that leads to a non-trivial symmetry breaking…
We propose an efficient stochastic method to implement numerically the Bogolubov approach to study finite-temperature Bose-Einstein condensates. Our method is based on the Wigner representation of the density matrix describing the non…