Related papers: Number-conserving solution for dynamical quantum b…
We discuss the response of a Bose-Einstein condensate to a change in the scattering length, which is experimentally realized by tuning the magnetic field near a Feshbach resonance. In particular, we consider the collapse of the condensate…
In this work we investigate the quantum dynamics of a model for two single-mode Bose--Einstein condensates which are coupled via Josephson tunneling. Using direct numerical diagonalisation of the Hamiltonian, we compute the time evolution…
We investigate the quantum dynamics of a harmonically trapped particle (e.g. an ion) that is immersed in a Bose--Einstein condensate. The ultracold environment acts as a refrigerator, and thus, the influence on the motion of the ion is…
We consider a system of $N$ bosons interacting through a singular two-body potential scaling with $N$ and having the form $N^{3\beta-1} V (N^\beta x)$, for an arbitrary parameter $\beta \in (0,1)$. We provide a norm-approximation for the…
We extend the Gross-Pitaevskii equation to incorporate the effect of quantum fluctuations onto the flow of a weakly interacting Bose-Einstein condensate. Applying this framework to an analog black hole in a quasi-one-dimensional, transonic…
In the setting of the principle of local equilibrium which asserts that the temperature is a function of the energy levels of the system, we exhibit plenty of steady states describing the condensation of free Bosons which are not in thermal…
We investigate the conditions under which quantum fluctuations are relevant for the quantitative interpretation of experiments with ultracold Bose gases. This requires to go beyond the description in terms of the Gross-Pitaevskii and…
Systems close to a phase transition turn weak perturbations into large responses. At equilibrium, this amplification is closely linked to criticality: fluctuations grow, dynamics slow, and a common soft mode controls the response. Whether…
We investigate the parametric amplification of the zero-point fluctuations in the spin modes of a two-component Bose-Einstein condensate, triggered by the dynamical evolution of the condensate density. We first make use of a Thomas-Fermi…
The paper is a continuation of our previous work on the spatially homogeneous Boltzmann equation for Bose-Einstein particles with quantum collision kernel that includes the hard sphere model. Solutions $F_t$ under consideration that…
Evading the Mermin-Wagner-Hohenberg no-go theorem and revisiting with rigor the ideal Bose gas confined in a square box, we explore a discrete phase transition in two spatial dimensions. Through both analytic and numerical methods we verify…
Using recently developed nonrelativistic numerical simulation code, we investigate the stability properties of compact astrophysical objects that may be formed due to the Bose-Einstein condensation of dark matter. Once the temperature of a…
We present a generalized Gross-Pitaevskii equation that describes also the dissipative dynamics of a trapped partially Bose condensed gas. It takes the form of a complex nonlinear Schr\"odinger equation with noise. We consider an…
We consider a Bose-Einstein condensate subject to a rotating harmonic potential, in connection with recent experiments leading to the formation of vortices. We use the classical hydrodynamic approximation to the non-linear Schr\"odinger…
We present the quantum theory for the nucleation of Bose-Einstein condensation in a dilute atomic Bose gas. This quantum theory comfirms the results of the semiclassical treatment, but has the important advantage that both the kinetic and…
Analyzing a Gross-Pitaevskii equation with cubic, quartic, and quintic nonlinearities through analytical and numerical methods, we examine the stability of two-dimensional (2D) trapless Bose-Einstein condensates (BECs) with two-, three-body…
Asymptotic behavior of a class of nonlinear Schr\"odinger equations are studied. Particular cases of 1D weakly focusing and Bose-Einstein condensates are considered. A statistical approach is presented to describe the stationary probability…
We numerically model decaying quantum turbulence in two-dimensional disk-shaped Bose-Einstein condensates, and investigate the effects of finite temperature on the turbulent dynamics. We prepare initial states with a range of condensate…
Recent experiments have revealed that beyond-mean-field corrections are much more relevant in weakly-interacting dipolar condensates than in their non-dipolar counterparts. We show that in quasi-one-dimensional geometries quantum…
We study the dynamics of two interacting Bose-Einstein condensates, by numerically solving two coupled Gross-Pitaevskii equations at zero temperature. We consider the case of a sudden transfer of atoms between two trapped states with…