Results 41 to 50 of about 32,263 (260)
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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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 $i \partial_t u = u + \varepsilon^{-2} u (1 - |u|^2)$ 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 $\varepsilon$. By carefully tracking errors we allow
Jerrard, Robert L., Spirn, Daniel
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The Timescales of Quantum Breaking
Fortschritte der Physik, Volume 71, Issue 12, December 2023., 2023 Abstract Due to the inevitable existence of quantum effects, a classical description generically breaks down after a finite quantum break‐time tq$t_q$. We aim to find criteria for determining tq$t_q$. To this end, we construct a new prototype model that features numerous dynamically accessible quantum modes.
Marco Michel, Sebastian Zell
wiley +1 more source
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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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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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
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q-Deformed Gross Pitaevskii Equation
, 2023 We derive the Gross Pitaevskii equation (GPE) for condensate of bosons obeying deformed statistics under external potential and inter-particle interaction. First, we obtain the well-known Schrodinger equation. Using a suitable Hamiltonian for condensate phase and minimizing the free energy of the system, we find out the $q$- deformed GPE. Thus, at very
Maleki, Mahnaz, Mohammadzadeh, Hosein
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Low-dimensional stochastic projected Gross-Pitaevskii equation [PDF]
Physical Review A, 2015 We present reduced-dimensional stochastic projected Gross-Pitaevskii equations describing regimes of confinement and temperature where a 1D or 2D superfluid is immersed in a 3D thermal cloud. The projection formalism provides both a formally rigorous and physically natural way to effect the dimensional reduction.
Bradley, A. S. +2 more
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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
semanticscholar +1 more source