The crystallization conjecture: a review

M Lewin, X Blanc - EMS Surveys in Mathematical Sciences, 2015 - ems.press
In this article we describe the crystallization conjecture. It states that, in appropriate physical
conditions, interacting particles always place themselves into periodic configurations …

GPELab, a Matlab toolbox to solve Gross–Pitaevskii equations I: Computation of stationary solutions

X Antoine, R Duboscq - Computer Physics Communications, 2014 - Elsevier
Abstract This paper presents GPELab (Gross–Pitaevskii Equation Laboratory), an advanced
easy-to-use and flexible Matlab toolbox for numerically simulating many complex physics …

Scalar Auxiliary Variable/Lagrange multiplier based pseudospectral schemes for the dynamics of nonlinear Schrödinger/Gross-Pitaevskii equations

X Antoine, J Shen, Q Tang - Journal of Computational Physics, 2021 - Elsevier
In this paper, based on the Scalar Auxiliary Variable (SAV) approach [44],[45] and a newly
proposed Lagrange multiplier (LagM) approach [22],[21] originally constructed for gradient …

On Optimal Convergence Rates for Discrete Minimizers of the Gross–Pitaevskii Energy in Localized Orthogonal Decomposition Spaces

P Henning, A Persson - Multiscale Modeling & Simulation, 2023 - SIAM
In this paper we revisit a two-level discretization based on localized orthogonal
decomposition (LOD). It was originally proposed in [P. Henning, A. Målqvist, and D …

GPELab, a Matlab toolbox to solve Gross–Pitaevskii equations II: Dynamics and stochastic simulations

X Antoine, R Duboscq - Computer Physics Communications, 2015 - Elsevier
GPELab is a free Matlab toolbox for modeling and numerically solving large classes of
systems of Gross–Pitaevskii equations that arise in the physics of Bose–Einstein …

Efficient spectral computation of the stationary states of rotating Bose–Einstein condensates by preconditioned nonlinear conjugate gradient methods

X Antoine, A Levitt, Q Tang - Journal of Computational Physics, 2017 - Elsevier
We propose a preconditioned nonlinear conjugate gradient method coupled with a spectral
spatial discretization scheme for computing the ground states (GS) of rotating Bose–Einstein …

A friendly review of absorbing boundary conditions and perfectly matched layers for classical and relativistic quantum waves equations

X Antoine, E Lorin, Q Tang - Molecular Physics, 2017 - Taylor & Francis
The aim of this paper is to describe concisely the recent theoretical and numerical
developments concerningabsorbing boundary conditions and perfectly matched layers for …

Super-localised wave function approximation of Bose-Einstein condensates

D Peterseim, J Wärnegård, C Zimmer - Journal of Computational Physics, 2024 - Elsevier
This paper presents a novel spatial discretisation method for reliable and efficient simulation
of Bose-Einstein condensates modelled by the Gross-Pitaevskii equation and the …

Computation of ground states of the Gross--Pitaevskii functional via Riemannian optimization

I Danaila, B Protas - SIAM Journal on Scientific Computing, 2017 - SIAM
In this paper we combine concepts from Riemannian optimization P.-A. Absil, R. Mahony,
and R. Sepulchre, Optimization Algorithms on Matrix Manifolds, Princeton University Press …

Mean-field limit of Bose systems: rigorous results

M Lewin - arXiv preprint arXiv:1510.04407, 2015 - arxiv.org
We review recent results about the derivation of the Gross-Pitaevskii equation and of the
Bogoliubov excitation spectrum, starting from many-body quantum mechanics. We focus on …