Related papers: Efficient numerical methods for computing ground s…
We investigate the mean-field dynamics of a Bose-Einstein condensate (BEC) described by the Gross-Pitaevskii equation (GPE) in a double-well potential with particle gain and loss, rendering the system PT-symmetric. The stationary solutions…
We propose the construction of a set of quantum hydrodynamics equations for the Bose-Einstein condensate (BEC) where atoms have electric dipole moment (EDM). The contribution of the dipole-dipole interactions (DDI) to the Euler equation is…
By exact numerical solutions of the Gross-Pitaevskii (GP) equation in 3D, we assess the validity of 1D and 2D approximations in the study of Bose-Einstein condensates confined in harmonic trap potentials. Typically, these approximations are…
We theoretically study the stability of a trapless dipolar Bose-Einstein condensate (BEC) with temporal modulation of short-range contact interaction. For this aim, through both analytical and numerical methods, we solve a Gross-Pitaevskii…
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 study dipolar Bose-Einstein condensates for a realistic set of parameters close to actual experimental setups with dysprosium. Our analysis is based on the extended Gross-Pitaevskii equation, which we solve numerically exact on a…
Open quantum systems theory is central to describing the dynamics and equilibration of dilute-gas Bose-Einstein condensates (BECs). We present an analysis of the linearized stochastic projected Gross-Pitaevskii equation (SPGPE) describing…
In this paper, we propose a regularized Newton method for computing ground states of Bose-Einstein condensates (BECs), which can be formulated as an energy minimization problem with a spherical constraint. The energy functional and…
The Gross-Pitaevskii equation (GPE) plays an important role in the description of Bose-Einstein condensates (BECs) at the mean-field level. The GPE belongs to the class of non-linear Schr\"odinger equations which are known to feature…
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…
We formulate a generalized self-consistent stochastic quantum kinetic theory for finite-temperature ultracold Bose gases interacting via a generic long-range interaction, applicable to a broad range of systems, by means of Keldysh…
This work presents a new methodology for computing ground states of Bose-Einstein condensates based on finite element discretizations on two different scales of numerical resolution. In a pre-processing step, a low-dimensional (coarse)…
In this paper, we prove the energy diminishing of a normalized gradient flow which provides a mathematical justification of the imaginary time method used in physical literatures to compute the ground state solution of Bose-Einstein…
This paper addresses the computation of ground states of multicomponent Bose-Einstein condensates, defined as the global minimiser of an energy functional on an infinite-dimensional generalised oblique manifold. We establish the existence…
The year 2025 marks the 100 and 30 years anniversaries of the discovery of Bose--Einstein condensation and its successful experimental realisation. Inspired by these important research achievements, a conceptually simple approach is…
We revisit the problem of the reduction of the three-dimensional (3D) dynamics of Bose-Einstein condensates, under the action of strong confinement in one direction ($z$), to a 2D mean-field equation. We address this problem for the…
We propose a normalized deep neural network (norm-DNN) for computing ground states of Bose-Einstein condensation (BEC) via the minimization of the Gross-Pitaevskii energy functional under unitary mass normalization. Compared with the…
We study the formation of singularities for cylindrical symmetric solutions to the Gross-Pitaevskii equation describing a dipolar Bose-Einstein condensate. We prove that solutions arising from initial data with energy below the energy of…
We study the stability of singly- and doubly-quantized vortex states of harmonically trapped dipolar Bose-Einstein Condensates (BECs) by calculating the low-lying excitations of these condensates. We map the dynamical stability of these…
Bubble-shaped Bose-Einstein condensates (BECs) constitute a unique class of quantum fluids with a hollow, thin-shell geometry that supports a wide variety of phenomena that are distinct from those of compact condensates. Numerical…