Related papers: Computable Error Estimates for Ground State Soluti…
This paper studies the localization behaviour of Bose-Einstein condensates in disorder potentials, modeled by a Gross-Pitaevskii eigenvalue problem on a bounded interval. In the regime of weak particle interaction, we are able to quantify…
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…
We prove that the Gross-Pitaevskii equation correctly describes the ground state energy and corresponding one-particle density matrix of rotating, dilute, trapped Bose gases with repulsive two-body interactions. We also show that there is…
We extend the Projected Gross Pitaevskii equation formalism of Davis et al. [Phys. Rev. Lett. \bf{87}, 160402 (2001)] to the experimentally relevant case of harmonic potentials. We outline a robust and accurate numerical scheme that can…
New efficient and accurate numerical methods are proposed to compute ground states and dynamics of dipolar Bose-Einstein condensates (BECs) described by a three-dimensional (3D) Gross-Pitaevskii equation (GPE) with a dipolar interaction…
The achievement of Bose-Einstein condensation (BEC) in ultracold vapors of alkali atoms has given enormous impulse to the theoretical and experimental study of dilute atomic gases in condensed quantum states inside magnetic traps and…
Dilute Bose gases, cooled down to low temperatures below the Bose-Einstein condensation temperature, form coherent ensembles described by the Gross-Pitaevskii equation. Stationary solutions to the latter are topological coherent modes. The…
In this article, we study mathematically and numerically the ground states of three-component rotating spin-orbit coupled (SOC) spin-1 Bose-Einstein condensates modeled by the coupled Gross-Pitaevskii equations (CGPEs). Firstly, we…
We propose a preconditioned nonlinear conjugate gradient method coupled with a spectral spatial dis-cretization scheme for computing the ground states (GS) of rotating Bose-Einstein condensates (BEC), modeled by the Gross-Pitaevskii…
We present a method for evolving the projected Gross-Pitaevskii equation in an infinite rotating Bose-Einstein condensate, the ground state of which is a vortex lattice. We use quasi-periodic boundary conditions to investigate the behaviour…
We show that both single-component and two-component Bose-Einstein condensates' (BECs) ground states can be simulated by deep convolutional neural networks of the same structure. We trained the neural network via inputting the coupling…
The diffusion Monte Carlo method is applied to describe a trapped atomic Bose-Einstein condensate at zero temperature, fully quantum mechanically and nonperturbatively. For low densities, $n(0)a^3 \le 2 \cdot 10^{-3}$ [n(0): peak density,…
We investigate a computational device that harnesses the effects of Bose-Einstein condensation (BEC) to accelerate the speed of finding the solution of a given optimization problem. Many computationally difficult problems, including…
We derive the Gross Pitaevskii equation (GPE) for condensate of bosons obeying deformed statistics under external potential and inter-particle interaction. First, we obtain the well-known Schrodinger equation. Using a suitable Hamiltonian…
Recent experimental breakthroughs in the treatment of dilute Bose gases have renewed interest in their quantum mechanical description, respectively in approximations to it. The ground state properties of dilute Bose gases confined in…
In this paper, we present a systematic study on the ground state computation of quantum droplets in homonuclear Bose-Bose mixtures, governed by the extended Gross-Pitaevskii equations (eGPEs) with Lee-Huang-Yang (LHY) corrections. This…
We derive the Gross-Pitaevskii equation in two-dimension from the first principles of two-dimensional scattering theory. Numerical calculation of the condensate wave function shows that atoms in a two-dimensional harmonic trap can be…
This paper is concerned with the computable error estimates for the eigenvalue problem which is solved by the general conforming finite element methods on the general meshes. Based on the computable error estimate, we can give an…
We study the numerical solution of the time-dependent Gross-Pitaevskii equation (GPE) describing a Bose-Einstein condensate (BEC) at zero or very low temperature. In preparation for the numerics we scale the 3d Gross-Pitaevskii equation and…
We review some mathematical work on the Bose gas in the Gross-Pitaevskii regime. We start with the classical results by Lieb, Seiringer and Yngvason on the ground state energy and by Lieb and Seiringer on the existence of Bose-Einstein…