Related papers: Generalized coherent state representation of Bose-…
We present results on Bose-Einstein condensation (BEC) on general compact quantum graphs, i.e., one-dimensional systems with a (potentially) complex topology. We first investigate non-interacting many-particle systems and provide a complete…
We study numerically the time-independent vector Gross-Pitaevskii equations (VGPEs) for ground states and time-dependent VGPEs with (or without) an external driven field for dynamics describing a multi-component Bose-Einstein condensate…
We consider Bose--Einstein condensation (BEC) on graphs with transient adjacency matrix and obtain a quasi-free state exhibiting BEC is non-factor and decompose into generalized coherent states. We review necessary and sufficient conditions…
We discuss the mean-field approximation for a trapped weakly-interacting Bose-Einstein condensate (BEC) and its connection with the exact many-body problem by deriving the Gross-Pitaevskii action of the condensate. The mechanics of the BEC…
Several authors have considered the possibility of a generalized Bose-Einstein condensation (BEC) in which a band of low states is occupied so that the total occupation number is macroscopic, even if the occupation number of each state is…
As an atomic Bose Einstein condensate (BEC) is coupled to a source of uncondensed atoms at the same temperature and to a sink (extraction towards an atom laser) the idealized description in terms of a Gross-Pitaevsky equation (GP) no longer…
In this article, we use quasifree reduction to derive the time-dependent Hartree-Fock-Bogoliubov (HFB) equations describing the dynamics of quantum fluctuations around a Bose-Einstein condensate in $\mathbb R^d$. We prove global…
Generalized Bose-Einstein condensation (GBEC) involves condensates appearing simultaneously in multiple states. We review examples of the three types in an ideal Bose gas with different geometries. In Type I there is a discrete number of…
We encode the many-body wavefunction of a Bose-Einstein condensate (BEC) in the $N$-particle sector of an extended catalytic state. This catalytic state is a coherent state for the condensate mode and an arbitrary state for the modes…
The Bogoliubov-de Gennes equations are used for a number of theoretical works on the trapped Bose-Einstein condensates. These equations are known to give the energies of the quasi-particles when all the eigenvalues are real. We consider the…
We apply the time-dependent generalized Hartree-Fock-Bogoliubov (td-GHFB) theory to describe the stimulated excitation driven by periodically modulating the interactions in a Bose-Einstein condensate (BEC). A comparison with the results…
We study the expansion of repulsively interacting Bose-Einstein condensates (BECs) in shallow one-dimensional potentials. We show for these systems that the onset of wave chaos in the Gross-Pitaevskii equation (GPE), i.e. the onset of…
The dynamics of matter-wave solitons in Bose-Einstein condensates (BEC) is considerably affected by the presence of a surrounding thermal cloud and by condensate depletion during its evolution. We analyze these aspects of BEC soliton…
We present a survey of macroscopic excitations of harmonically confined Bose-Einstein condensates (BEC), described by Gross-Pitaevskii (GP) equation, in search of routes to develop quantum turbulence. These excitations can all be created by…
We investigate the dynamics of a homogenous Bose-Einstein condensate (BEC) following a sudden quench of the scattering length. Our focus is the time evolution of short-range correlations via the dynamical contact. We compute the dynamics…
Self-gravitating Bose-Einstein condensates (BEC) have been proposed in various astrophysical contexts, including Bose-stars and BEC dark matter halos. These systems are described by a combination of the Gross-Pitaevskii and Poisson…
We consider the possible existence of gravitationally bound general relativistic strings consisting of Bose-Einstein condensate (BEC) matter which is described, in the Newtonian limit, by the zero temperature time-dependent nonlinear…
We derive the dynamic and thermodynamic stability conditions for dilute multicomponent Bose-Einstein condensates (BECs). These stability conditions, generalized for $n$-component BECs, are found to be equivalent and are shown to be…
We obtain approximations for the time-independent Gross-Pitaevskii (GP) and complex GP equation in two and three spatial dimensions by generalizing the divergence-free WKB method. The results include an explicit expression of a uniformly…
The non-linear coupled Gross-Pitaevskii equation governing the dynamics of the two component Bose-Einstein condensate (TBEC) is shown to admit pure sinusoidal, propagating wave solutions in quasi one dimensional geometry. These solutions,…