The Finite Element Method for the time-dependent Gross-Pitaevskii equation with angular momentum rotation [PDF]
, 2016 We consider the time-dependent Gross-Pitaevskii equation describing the dynamics of rotating Bose-Einstein condensates and its discretization with the finite element method.
Henning, Patrick, Målqvist, Axel
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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 ...
J. Bellazzini, D. Ruiz
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Scattering for the Gross-Pitaevskii equation [PDF]
Mathematical Research Letters, 2006 We investigate the asymptotic behavior at time infinity of solutions close to a non-zero constant equilibrium for the Gross-Pitaevskii (or Ginzburg-Landau Schroedinger) equation. We prove that, in dimensions larger than 3, small perturbations can be approximated at time infinity by the linearized evolution, and the wave operators are homeomorphic ...
Gustafson, S. +2 more
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Continuous quantum measurement of a Bose-Einstein condensate: a stochastic Gross-Pitaevskii equation [PDF]
, 2001 We analyze the dynamics of a Bose-Einstein condensate undergoing a continuous dispersive imaging by using a Lindblad operator formalism. Continuous strong measurements drive the condensate out of the coherent state description assumed within the Gross ...
Dalvit, Diego A. R. +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
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Formal analytical solutions for the Gross–Pitaevskii equation [PDF]
Physica D: Nonlinear Phenomena, 2008 8 ...
Trallero-Giner, C. +3 more
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Hybrid OpenMP/MPI programs for solving the time-dependent Gross-Pitaevskii equation in a fully anisotropic trap [PDF]
Computer Physics Communications, 2016 We present hybrid OpenMP/MPI (Open Multi-Processing/Message Passing Interface) parallelized versions of earlier published C programs (Vudragovic et al.
B. Sataric +5 more
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Unconditional uniqueness for the energy-critical nonlinear Schrödinger equation on $\mathbb {T}^{4}$
Forum of Mathematics, Pi, 2022 We consider the $\mathbb {T}^{4}$ cubic nonlinear Schrödinger equation (NLS), which is energy-critical. We study the unconditional uniqueness of solutions to the NLS via the cubic Gross–Pitaevskii hierarchy, an uncommon method for NLS analysis which is ...
Xuwen Chen, Justin Holmer
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, 2004 We give here the derivation of a Gross-Pitaevskii--type equation for inhomogeneous condensed bosons. Instead of the original Gross-Pitaevskii differential equation, we obtain an integral equation that implies less restrictive assumptions than are made in
A. J. Leggett +9 more
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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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