Results 11 to 20 of about 3,107,805 (229)
Finite energy traveling waves for the Gross-Pitaevskii equation in the subsonic regime [PDF]
American Journal of Mathematics, 2019 :In this paper we study the existence of finite energy traveling waves for the Gross-Pitaevskii equation. This problem hasdeserved a lot of attention in the literature, but the existence of solutions in the whole subsonic range was a standing open ...
Jacopo Bellazzini, David Ruiz
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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 +4 more
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Nonlinear quantum search using the Gross–Pitaevskii equation
New Journal of Physics, 2013 We solve the unstructured search problem in constant time by computing with a physically motivated nonlinearity of the Gross–Pitaevskii type. This speedup comes, however, at the novel expense of increasing the time-measurement precision.
David A Meyer, Thomas G Wong
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Remarks on the derivation of Gross-Pitaevskii equation with magnetic Laplacian [PDF]
, 2017 The effective dynamics for a Bose-Einstein condensate in the regime of high dilution and subject to an external magnetic field is governed by a magnetic Gross-Pitaevskii equation.
A. Knowles +4 more
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Travelling waves for the Gross-Pitaevskii equation II [PDF]
, 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 +34 more
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Quantum fluctuations of many-body dynamics around the Gross–Pitaevskii equation [PDF]
Annales de l'Institut Henri Poincare. Analyse non linéar, 2023 We consider the evolution of a gas of $N$ bosons in the three-dimensional Gross-Pitaevskii regime (in which particles are initially trapped in a volume of order one and interact through a repulsive potential with scattering length of the order $1/N$). We
Cristina Caraci +2 more
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Uniform L∞-bounds for energy-conserving higher-order time integrators for the Gross-Pitaevskii equation with rotation [PDF]
IMA Journal of Numerical Analysis, 2022 In this paper, we consider an energy-conserving continuous Galerkin discretization of the Gross–Pitaevskii equation with a magnetic trapping potential and a stirring potential for angular momentum rotation.
Christian Döding, P. Henning
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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
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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
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Results in Physics, 2023 This study applies computational and numerical techniques to develop some novel and accurate solutions for Gross–Pitaevskii (GP) equations. A quantum system of identical bosons is described using the Hartree–Fock approximation and pseudopotential ...
Mostafa M.A. Khater +3 more
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