Results 21 to 30 of about 1,617,592 (202)
Travelling Waves for the Gross-Pitaevskii Equation II
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. Our arguments, based on minimization under constraints, yield a full branch of solutions, and extend earlier results, where only a part of the branch was built.
Bethuel, Fabrice +2 more
openaire +7 more sources
Superconvergence of time invariants for the Gross–Pitaevskii equation [PDF]
Mathematics of Computation, 2021 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 suitable generalized finite element discretization in space.
Patrick Henning, Johan Wärnegård
openaire +3 more sources
Quantitative Derivation of the Gross‐Pitaevskii Equation [PDF]
Communications on Pure and Applied Mathematics, 2014 Starting from first‐principle many‐body quantum dynamics, we show that the dynamics of Bose‐Einstein condensates can be approximated by the time‐dependent nonlinear Gross‐Pitaevskii equation, giving a bound on the rate of the convergence. Initial data are constructed on the bosonic Fock space applying an appropriate Bogoliubov transformation on a ...
Benedikter N, de Oliveira G, Schlein B
openaire +4 more sources
The inverse problem for the Gross–Pitaevskii equation [PDF]
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2010 Two different methods are proposed for the generation of wide classes of exact solutions to the stationary Gross–Pitaevskii equation (GPE). The first method, suggested by the work of Kondrat’ev and Miller [Izv. Vyssh. Uchebn. Zaved., Radiofiz IX, 910 (1966)], applies to one-dimensional (1D) GPE.
Malomed, Boris A., Stepanyants, Yury A.
openaire +5 more sources
Stochastic projected Gross-Pitaevskii equation [PDF]
Physical Review A, 2012 We have achieved the first full implementation of the stochastic projected Gross-Pitaevskii equation for a three-dimensional trapped Bose gas at finite temperature. Our work advances previous applications of this theory, which have only included growth processes, by implementing number-conserving scattering processes. We evaluate an analytic expression
Rooney, S. J. +2 more
openaire +2 more sources
Hydrodynamic Limit of the Gross-Pitaevskii Equation [PDF]
Communications in Partial Differential Equations, 2014 We study dynamics of vortices in solutions of the Gross-Pitaevskii equation $i \partial_t u = Δu + \varepsilon^{-2} u (1 - |u|^2)$ on $\mathbb{R}^2$ with nonzero degree at infinity. We prove that vortices move according to the classical Kirchhoff-Onsager ODE for a small but finite coupling parameter $\varepsilon$.
Jerrard, Robert L., Spirn, Daniel
openaire +2 more sources
Vortices in nonlocal Gross–Pitaevskii equation [PDF]
Journal of Physics A: Mathematical and General, 2004 Second revision: small changes; 23 pages; 8 ...
Shchesnovich, V. S. +1 more
openaire +3 more sources
Scattering for the 3D Gross–Pitaevskii Equation [PDF]
Communications in Mathematical Physics, 2017 28 pages; Correct some mistakes, the main results remain the ...
Guo, Zihua +2 more
openaire +2 more sources
Energy eigenfunctions of the 1D Gross–Pitaevskii equation [PDF]
Computer Physics Communications, 2013 18 pages, 11 ...
Zelimir Marojevic +2 more
openaire +2 more sources
Semiclassical Spectral Series Localized on a Curve for the Gross–Pitaevskii Equation with a Nonlocal Interaction [PDF]
, 2021 We propose the approach to constructing semiclassical spectral series for the generalized multidimensional stationary Gross–Pitaevskii equation with a nonlocal interaction term.
Anton E. Kulagin +8 more
core +1 more source