Semiclassical solutions localized in a neighborhood of a circle for the Gross-Pitaevskii equation [PDF]
Компьютерные исследования и моделирование, 2009 Non-collapsing soliton-like wave functions are shown to exist in semiclassical approximation for the Bose-Einstein condensate model based on the Gross-Pitaevskii equation with attractive nonlinearity and external field of magnetic trap of special form.
Aleksei Vladimirovich Borisov +2 more
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Evolution of Bose–Einstein condensate systems beyond the Gross–Pitaevskii equation
Frontiers in Physics, 2023 While many phenomena in cold atoms and other Bose–Einstein condensate (BEC) systems are often described using the mean-field approaches, understanding the kinetics of BECs requires the inclusion of particle scattering via the collision integral of the ...
Yuli Lyanda-Geller, Yuli Lyanda-Geller
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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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Optimal Bilinear Control of Gross--Pitaevskii Equations [PDF]
SIAM Journal on Control and Optimization, 2013 A mathematical framework for optimal bilinear control of nonlinear Schrödinger equations of Gross-Pitaevskii type arising in the description of Bose-Einstein condensates is presented. The obtained results generalize earlier efforts found in the literature in several aspects.
Michael Hintermüller +3 more
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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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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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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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Turbulence in the two-dimensional Fourier-truncated Gross–Pitaevskii equation
New Journal of Physics, 2013 We undertake a systematic, direct numerical simulation of the two-dimensional, Fourier-truncated, Gross–Pitaevskii equation to study the turbulent evolutions of its solutions for a variety of initial conditions and a wide range of parameters.
Vishwanath Shukla +2 more
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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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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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