Results 11 to 20 of about 32,263 (260)
Rigorous Derivation of the Gross-Pitaevskii Equation [PDF]
Physical Review Letters, 2006 The time dependent Gross-Pitaevskii equation describes the dynamics of initially trapped Bose-Einstein condensates. We present a rigorous proof of this fact starting from a many-body bosonic Schroedinger equation with a short scale repulsive interaction ...
Benjamin Schlein +4 more
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Travelling waves for the Gross-Pitaevskii equation II [PDF]
Communications in Mathematical Physics, 2008 The purpose of this paper is to provide a rigorous mathematical proof of the existence of travelling wave solutions to the Gross-Pitaevskii equation in dimensions two and three.
A. Bouard de +34 more
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Logarithmic Gross-Pitaevskii equation [PDF]
Communications in Partial Differential Equations, 2022 We consider the Schrödinger 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 ...
R. Carles, G. Ferriere
semanticscholar +4 more sources
Derivation of the Gross-Pitaevskii equation for the dynamics of Bose-Einstein condensate [PDF]
, 2010 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
László Erdős +2 more
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Deriving the Gross-Pitaevskii equation [PDF]
Mathematical Results in Quantum Mechanics, 2014 In experiments, Bose-Einstein condensates are prepared by cooling a dilute Bose gas in a trap. After the phase transition has been reached, the trap is switched off and the evolution of the condensate observed.
Benedikter, Niels
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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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Complex soliton wave patterns of Gross–Pitaevskii systems: application in quantum and optical engineering [PDF]
Scientific ReportsThe purpose of this work is to explore precise solutions, particularly soliton solutions, by fractionally analyzing the multicomponent Gross–Pitaevskii problem, a basic nonlinear Schrödinger equation. Soliton solutions are essential for comprehending the
Muhammad Bilal +5 more
doaj +2 more sources
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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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 $\
Ko‐Shin Chen
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Quantitative Derivation of the Gross‐Pitaevskii Equation [PDF]
Communications on Pure and Applied Mathematics, 2012 Starting from first‐principle many‐body quantum dynamics, we show that the dynamics of Bose‐Einstein condensates can be approximated by the time‐dependent nonlinear Gross‐Pitaevskii equation, giving a bound on the rate of the convergence.
Niels Benedikter +2 more
semanticscholar +5 more sources