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 …
conditions, interacting particles always place themselves into periodic configurations …
GPELab, a Matlab toolbox to solve Gross–Pitaevskii equations I: Computation of stationary solutions
Abstract This paper presents GPELab (Gross–Pitaevskii Equation Laboratory), an advanced
easy-to-use and flexible Matlab toolbox for numerically simulating many complex physics …
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
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 …
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 …
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
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 …
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
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 …
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
The aim of this paper is to describe concisely the recent theoretical and numerical
developments concerningabsorbing boundary conditions and perfectly matched layers for …
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 …
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 …
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 …
Bogoliubov excitation spectrum, starting from many-body quantum mechanics. We focus on …