Results 11 to 20 of about 1,617,592 (202)
Logarithmic Gross-Pitaevskii equation [PDF]
Communications in Partial Differential Equations, 2023 We consider the Schr{ö}dinger 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 standard Gross-Pitaevskii equation with a cubic nonlinearity, in small dimensions.
Carles, Rémi, Ferriere, Guillaume
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The stochastic Gross–Pitaevskii equation: II [PDF]
Journal of Physics B: Atomic, Molecular and Optical Physics, 2003 We provide a derivation of a more accurate version of the stochastic Gross-Pitaevskii equation, as introduced by Gardiner et al. (J. Phys. B 35,1555,(2002). The derivation does not rely on the concept of local energy and momentum conservation, and is based on a quasi-classical Wigner function representation of a "high temperature" master equation for a
Gardiner, C. W., Davis, M. J.
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Vortex helices for the Gross–Pitaevskii equation [PDF]
Journal de Mathématiques Pures et Appliquées, 2005 We prove the existence of travelling vortex helices to the Gross-Pitaevskii equation in R^3. These solutions have an infi nite energy, are periodic in the direction of the axis of the helix and have a degree one at infinity in the orthogonal direction.
David Chiron, Chiron, David
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Rigorous Derivation of the Gross-Pitaevskii Equation [PDF]
Physical Review Letters, 2007 4 pages, 1 ...
Erdős, László +2 more
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The Gross–Pitaevskii equation and Bose–Einstein condensates [PDF]
European Journal of Physics, 2013 The Gross-Pitaevskii equation is discussed at the level of an advanced course on statistical physics. In the standard literature the Gross-Pitaevskii equation is usually obtained in the framework of the second quantisation formalism, which in many cases goes beyond the material covered in many advanced undergraduate courses.
Rogel-Salazar, Jesus
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Stochastic fluctuations in the Gross–Pitaevskii equation [PDF]
Nonlinearity, 2007 Summary: We study from a mathematical point of view a model equation for a Bose-Einstein condensation, in the case where the trapping potential varies randomly in time. The model is the so-called Gross-Pitaevskii equation, with a quadratic potential with white noise fluctuations in time.
De Bouard, Anne, Fukuizumi, Reika
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The Gross–Pitaevskii equation: Bäcklund transformations and admitted solutions [PDF]
Ricerche di Matematica, 2018 Bäcklund transformations are applied to study the Gross-Pitaevskii equation. Supported by previous results, a class of Bäcklund transformations admitted by this equation are constructed. Schwartzian derivative as well as its invariance properties turn out to represent a key tool in the present investigation. Examples and explicit solutions of the Gross-
Carillo, Sandra, Zullo, Federico
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Finite volumes for the Gross-Pitaevskii equation
Journal of Computational and Applied MathematicsWe study the approximation by a semi-discrete finite-volume scheme of the Gross-Pitaevskii equation with time-dependent potential in two dimensions, performing a two-point flux approximation scheme in space. We rigorously analyze the error bounds relying on discrete uniform Sobolev inequalities.
Chauleur, Quentin
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On the linear wave regime of the Gross-Pitaevskii equation [PDF]
Journal d'Analyse Mathématique, 2010 We study a long wave-length asymptotics for the Gross-Pitaevskii equation corresponding to perturbation of a constant state of modulus one. We exhibit lower bounds on the first occurence of possible zeros (vortices) and compare the solutions with the corresponding solutions to the linear wave equation or variants.
Bethuel, Fabrice +2 more
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Dynamics of a Gross-Pitaevskii Equation with Phenomenological Damping [PDF]
International Journal of Differential Equations, 2013 We study the dynamical behavior of solutions of an n-dimensional nonlinear Schrödinger equation with potential and linear derivative terms under the presence of phenomenological damping.
Renato Colucci +2 more
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