Related papers: Particle-Number-Conserving Bogoliubov Approximatio…
This paper presents a novel spatial discretisation method for the reliable and efficient simulation of Bose-Einstein condensates modelled by the Gross-Pitaevskii equation and the corresponding nonlinear eigenvector problem. The method…
We show various aspects of finite size effects on Bose-Einstein condensation(BEC). In the first section we introduce very briefly the BEC of harmonically trapped ideal Bose gas. In the second section we theoretically argued that…
We use the time-dependent mean-field Gross-Pitaevskii equation to study the formation of a dynamically-stabilized dissipation-managed bright soliton in a quasi-one-dimensional Bose-Einstein condensate (BEC). Because of three-body…
We consider dilute Bose gases on the three dimensional unit torus that interact through a pair potential with scattering length of order $ N^{\kappa-1}$, for some $\kappa >0$. For the range $ \kappa\in [0, \frac1{43})$, \cite{ABS} proves…
The existence and stability of solitonic states in one-dimensional repulsive Bose-Einstein condensates is investigated within a fully many-body framework by considering the limit of infinite repulsion (Tonks-Girardeau gas). A class of…
The phases of a Bose-Einstein condensate (BEC) with light-induced spin-orbit coupling (SOC) are studied within the mean-field approximation. The mixed BEC phase, in which the system condenses in a superposition of two plane wave states, is…
The Gross-Pitaevskii (GP) equation is a long-wavelength approach widely used to describe the dilute Bose-Einstein condensates (BEC). However, in many physical situations, such as higher densities, this approximation unlikely suffices hence…
In three-dimensional trapped Bose-Einstein condensate (BEC), described by the time-dependent Gross-Pitaevskii-Ginzburg equation, we study the effect of initial conditions on stability using a Gaussian variational approach and exact…
The self-consistent equations for the order parameters of Bose-Einstein condensation (BEC) of molecules and Bardeen-Cooper-Schrieffer (BCS) condensation of atoms in a Fermi gas of atoms with an attractive two-body interaction between atoms…
Machine Learning methods are emerging as faster and efficient alternatives to numerical simulation techniques. The field of Scientific Computing has started adopting these data-driven approaches to faithfully model physical phenomena using…
We introduce dimensional perturbation techniques to Bose-Einstein condensation of inhomogeneous alkali gases (BEC). The perturbation parameter is delta=1/kappa, where kappa depends on the effective dimensionality of the condensate and on…
We derive an effective nonpolynomial Schrodinger equation (NPSE) for self-repulsive or attractive BEC in the nearly-1D cigar-shaped trap, with the transverse confining frequency periodically modulated along the axial direction. Besides the…
Gross-Pitaevskii equation with gain is used to model Bose Einstein condensation (BEC) fed by the surrounding thermal cloud. It is shown that the number of atoms continuously injected into BEC from the reservoir can be controlled by applying…
This work is concerned with the construction and analysis of structure-preserving Galerkin methods for computing the dynamics of rotating Bose-Einstein condensate (BEC) based on the Gross-Pitaevskii equation with angular momentum rotation.…
We provide a framework for turning a numerical simulation of a gap soliton in the one-dimensional Gross-Pitaevskii equation into a rigorous mathematical proof of its existence. These nonlinear localized solutions play a central role in the…
Most of the work done in the field of Bose-Einstein condensates with balanced gain and loss has been performed in the mean-field approximation using the PT-symmetric Gross-Pitaevskii equation. In this work we study the many-particle…
We derive the time-dependent two-component Gross--Pitaevskii (GP) equation as an effective description of the dynamics of a dilute two-component Bose gas near its ground state, which exhibits a two-component Bose-Einstein condensate, in the…
We obtain equations of quantum hydrodynamic (QHD) for magnetized spin-1 neutral Bose-Einstein condensate (BEC). System of QHD equations contains the equation of magnetic moment evolution (an analog of the Bloch equation). We account…
A condensate initially prepared at finite temperature evolves under external time-dependent perturbation into a time-dependent mixed state. In these notes I use number-conserving time-dependent Bogoliubov theory to derive probability…
We examine Bose-Einstein condensation (BEC) for particles trapped in a harmonic potential by considering it as a transition in the length of permutation cycles that arise from wave-function symmetry. This ``loop-gas'' approach was…