Conserved energies for the one dimensional Gross-Pitaevskii equation [PDF]
, 2019 We prove the global-in-time well-posedness of the one dimensional Gross-Pitaevskii equation in the energy space, which is a complete metric space equipped with a newly introduced metric and with the energy norm describing the $H^s$ regularities of the ...
Koch, Herbert, Liao, Xian
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Derivation of the Gross-Pitaevskii equation for the dynamics of Bose-Einstein condensate [PDF]
, 2004 Consider a system of N bosons in three dimensions interacting via a repulsive short range pair potential N 2 V (N(xi − xj)), where x = (x1, . . ., xN) denotes the positions of the particles. Let HN denote the Hamiltonian of the system and let ψN,t be the
L. Erdős, B. Schlein, H. Yau
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Two infinite families of resonant solutions for the Gross-Pitaevskii equation [PDF]
Physical Review E, 2018 We consider the two-dimensional Gross-Pitaevskii equation describing a Bose-Einstein condensate in an isotropic harmonic trap. In the small coupling regime, this equation is accurately approximated over long times by the corresponding nonlinear resonant ...
Anxo Biasi +3 more
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Beyond Gross-Pitaevskii equation for 1D gas: quasiparticles and solitons
SciPost Physics, 2022 Describing properties of a strongly interacting quantum many-body system poses a serious challenge both for theory and experiment. In this work, we study excitations of one-dimensional repulsive Bose gas for arbitrary interaction strength using a ...
Jakub Kopyciński, Maciej Łebek, Maciej Marciniak, Rafał Ołdziejewski, Wojciech Górecki, Krzysztof Pawłowski
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The Generalized Point-Vortex Problem and Rotating Solutions to the Gross-Pitaevskii Equation on Surfaces of Revolution [PDF]
, 2014 We study the generalized point-vortex problem and the Gross-Pitaevskii equation on surfaces of revolution. We find rotating periodic solutions to the generalized point-vortex problem, which have two two rings of $n$ equally spaced vortices with degrees $\
Chen, Ko-Shin
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Probing quasi-integrability of the Gross–Pitaevskii equation in a harmonic-oscillator potential [PDF]
Journal of Physics B: Atomic, Molecular and Optical Physics, 2018 Previous simulations of the one-dimensional Gross–Pitaevskii equation (GPE) with repulsive nonlinearity and a harmonic-oscillator trapping potential hint towards the emergence of quasi-integrable dynamics—in the sense of quasi-periodic evolution of a ...
Thomas Bland +3 more
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, 2020 An ultradilute quantum droplet is a self-bound liquidlike state recently observed in ultracold Bose-Einstein condensates. In most previous theoretical studies, it is described by a phenomenological low-energy effective theory, termed as the extended ...
Hui Hu, Xia-ji Liu
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Comparison of Splitting Methods for Deterministic/Stochastic Gross–Pitaevskii Equation
Mathematical and Computational Applications, 2019 In this paper, we discuss the different splitting approaches to numerically solvethe Gross–Pitaevskii equation (GPE). The models are motivated from spinor Bose–Einsteincondensate (BEC).
Jürgen Geiser, Amirbahador Nasari
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Linear "ship waves" generated in stationary flow of a Bose-Einstein condensate past an obstacle [PDF]
, 2006 Using stationary solutions of the linearized two-dimensional Gross-Pitaevskii equation, we describe the ``ship wave'' pattern occurring in the supersonic flow of a Bose-Einstein condensate past an obstacle.
A. Gammal +6 more
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Existence and nonexistence of traveling waves for the Gross-Pitaevskii equation in tori
Mathematics in Engineering, 2023 In this paper we consider traveling waves for the Gross-Pitaevskii equation which are $ T $-periodic in each variable. We prove that if $ T $ is large enough, there exists a solution as a global minimizer of the corresponding action functional.
Francisco Javier Martínez Sánchez +1 more
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