Results 11 to 20 of about 33,314 (234)

Rigorous Derivation of the Gross-Pitaevskii Equation [PDF]

Physical Review Letters, 2006
The time dependent Gross-Pitaevskii equation describes the dynamics of initially trapped Bose-Einstein condensates. We present a rigorous proof of this fact starting from a many-body bosonic Schroedinger equation with a short scale repulsive interaction ...
Benjamin Schlein, E. P. Gross, Horng-Tzer Yau, L. P. Pitaevskii, László Erdős   +4 more
core   +7 more sources

Travelling waves for the Gross-Pitaevskii equation II [PDF]

Communications in Mathematical Physics, 2008
The purpose of this paper is to provide a rigorous mathematical proof of the existence of travelling wave solutions to the Gross-Pitaevskii equation in dimensions two and three.
A. Bouard de, A. de Bouard, A. Farina, C.A. Jones, C.A. Jones, D. Chiron, E.P. Gross, F. Béthuel, F. Béthuel, Fabrice Béthuel, I. Ekeland, J.L. Bona, J.L. Bona, Jean-Claude Saut, K. Kato, L. Almeida, L.P. Pitaevskii, M. Maris, M. Maris, O. Goubet, O. Lopes, P. Gravejat, P. Gravejat, P. Gravejat, P. Gravejat, P. Gravejat, P. Gravejat, P. Gravejat, P. Gérard, P.I. Lizorkin, Philippe Gravejat, S. Gustafson, S. Gustafson, S.V. Iordanskii, É. Tarquini   +34 more
core   +10 more sources

Logarithmic Gross-Pitaevskii equation [PDF]

Communications in Partial Differential Equations, 2022
We consider the Schrödinger equation with a logarithmic nonlinearty and non-trivial boundary conditions at infinity. We prove that the Cauchy problem is globally well posed in the energy space, which turns out to correspond to the energy space for the ...
R. Carles, G. Ferriere
semanticscholar   +4 more sources

Superconvergence of time invariants for the Gross-Pitaevskii equation [PDF]

Mathematics of Computation, 2020
This paper considers the numerical treatment of the time-dependent Gross-Pitaevskii equation. In order to conserve the time invariants of the equation as accurately as possible, we propose a Crank-Nicolson-type time discretization that is combined with a
P. Henning, Johan Wärnegård
semanticscholar   +4 more sources

Deriving the Gross-Pitaevskii equation [PDF]

Mathematical Results in Quantum Mechanics, 2014
In experiments, Bose-Einstein condensates are prepared by cooling a dilute Bose gas in a trap. After the phase transition has been reached, the trap is switched off and the evolution of the condensate observed.
Benedikter, Niels
core   +3 more sources

Inverse scattering transformation and soliton stability for a nonlinear Gross–Pitaevskii equation with external potentials

Applied Mathematics Letters, 2019
We consider the Gross–Pitaevskii(GP) equation with the combination of periodic and harmonic external potentials. In particular, the method of inverse scattering transformation is applied to the GP equation with external potentials.
Fajun yu
exaly   +2 more sources

Solving the Gross-Pitaevskii equation on multiple different scales using the quantics tensor train representation

Physical Review Research
Solving partial differential equations across multiple length scales represents a formidable challenge where reaching high precision can require a prohibitive amount of computer memory or computing time.
Marcel Niedermeier, Adrien Moulinas, Thibaud Louvet, Jose L. Lado, Xavier Waintal   +4 more
doaj   +2 more sources

OpenMP Fortran and C programs for solving the time-dependent Gross–Pitaevskii equation in an anisotropic trap [PDF]

Computer Physics Communications, 2016
We present new version of previously published Fortran and C programs for solving the Gross–Pitaevskii equation for a Bose–Einstein condensate with contact interaction in one, two and three spatial dimensions in imaginary and real time, yielding both ...
Luis E Young-S, Dusan Vudragovic, Paulsamy Muruganandam   +2 more
exaly   +2 more sources

Dynamics of a Gross-Pitaevskii Equation with Phenomenological Damping [PDF]

International Journal of Differential Equations, 2013
We study the dynamical behavior of solutions of an n-dimensional nonlinear Schrödinger equation with potential and linear derivative terms under the presence of phenomenological damping.
Renato Colucci, Gerardo R. Chacón, Andrés Vargas   +2 more
doaj   +4 more sources

On the linear wave regime of the Gross-Pitaevskii equation [PDF]

Journal d'Analyse Mathématique, 2008
We study a long wave-length asymptotics for the Gross-Pitaevskii equation corresponding to perturbation of a constant state of modulus one. We exhibit lower bounds on the first occurence of possible zeros (vortices) and compare the solutions with the ...
Bethuel, Fabrice, Danchin, Raphael, Smets, Didier   +2 more
core   +7 more sources