相关论文: Computing the ground state solution of Bose-Einste…
In this paper, we propose an efficient and accurate numerical method for computing the ground state of spin-1 Bose-Einstein condensates (BEC) by using the normalized gradient flow or imaginary time method. The key idea is to find a third…
We propose and analyze an efficient and accurate numerical method for computing ground states of spin-2 Bose-Einstein condensates (BECs) by using the normalized gradient flow (NGF). In order to successfully extend the NGF to spin-2 BECs…
Second-order flows in this paper refer to some artificial evolutionary differential equations involving second-order time derivatives distinguished from gradient flows which are considered to be first-order flows. This is a popular topic…
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…
In this paper, we generalize the normalized gradient flow method to compute the ground states of Bose-Einstein condensates (BEC) with higher order interactions (HOI), which is modelled via the modified Gross-Pitaevskii equation (MGPE).…
This paper investigates numerical methods for approximating the ground state of Bose--Einstein condensates (BECs) by introducing two relaxed formulations of the Gross--Pitaevskii energy functional. These formulations achieve first- and…
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…
The gradient flow with semi-implicit discretization (GFSI) is the most widely used algorithm for computing the ground state of Gross-Pitaevskii energy functional. Numerous numerical experiments have shown that the energy dissipation holds…
In this paper, we mainly review recent results on mathematical theory and numerical methods for Bose-Einstein condensation (BEC), based on the Gross-Pitaevskii equation (GPE). Starting from the simplest case with one-component BEC of the…
In this paper, we propose a new numerical method to compute the ground state solution of trapped interacting Bose-Einstein condensation (BEC) at zero or very low temperature by directly minimizing the energy functional via finite element…
The computation of the ground states of spin-$F$ Bose-Einstein condensates (BECs) can be formulated as an energy minimization problem with two quadratic constraints. We discretize the energy functional and constraints using the Fourier…
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…
A numerical framework is proposed and analyzed for computing the ground state of Bose--Einstein condensates. A gradient flow approach is developed, incorporating both a Lagrange multiplier to enforce the $L^2$ conservation and a free energy…
We present a level-set based finite difference method to calculate the ground states of Bose Einstein condensates in domains with curved boundaries. Our method draws on the variational and level set approaches, benefiting from both of their…
We propose and analyze a new numerical method for computing the ground state of the modified Gross-Pitaevskii equation for modeling the Bose-Einstein condensate with a higher order interaction by adapting the density function formulation…
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 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…
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…
In this work, we consider the numerical computation of ground states and dynamics of single-component Bose-Einstein condensates (BECs). The corresponding models are spatially discretized with a multiscale finite element approach known as…
In this paper, we generalize the normalized gradient flow method which was first applied to computing the least energy ground state to compute the least action ground state. A continuous normalized gradient flow (CNGF) will be presented and…