Results 121 to 130 of about 33,314 (234)
Quantum field effects in coupled atomic and molecular Bose-Einstein condensates
, 2001 This paper examines the parameter regimes in which coupled atomic and molecular Bose-Einstein condensates do not obey the Gross-Pitaevskii equation. Stochastic field equations for coupled atomic and molecular condensates are derived using the functional ...
B. Levi +30 more
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Mathematische Nachrichten, Volume 297, Issue 10, Page 3870-3886, October 2024.Abstract The Gross–Pitaevskii (GP) equation is a model for the description of the dynamics of Bose–Einstein condensates. Here, we consider the GP equation in a two‐dimensional setting with an external periodic potential in the x$x$‐direction and a harmonic oscillator potential in the y$y$‐direction in the so‐called tight‐binding limit.
Steffen Gilg, Guido Schneider
wiley +1 more source
Multisymplectic Spectral Methods for the Gross-Pitaevskii Equation [PDF]
, 2002 Recently, Bridges and Reich introduced the concept of multisymplectic spectral discretizations for Hamiltonian wave equations with periodic boundary conditions [5]. In this paper, we show that the ID nonlinear Schrodinger equation and the 2D Gross-Pitaevskii equation are multi-symplectic and derive multi-symplectic spectral discretizations of these ...
Alvaro L. Islas, Constance M. Schober
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Complex Ginzburg–Landau equation for time‐varying anisotropic media
Studies in Applied Mathematics, Volume 153, Issue 3, October 2024.Abstract When extending the complex Ginzburg–Landau equation (CGLE) to more than one spatial dimension, there is an underlying question of whether one is capturing all the interesting physics inherent in these higher dimensions. Although spatial anisotropy is far less studied than its isotropic counterpart, anisotropy is fundamental in applications to ...
Robert A. Van Gorder
wiley +1 more source
Analytical Solution for the Gross-Pitaevskii Equation in Phase Space and Wigner Function
Advances in High Energy Physics, 2020 In this work, we study symplectic unitary representations for the Galilei group. As a consequence a nonlinear Schrödinger equation is derived in phase space.
A. X. Martins +6 more
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Hydrodynamical form for the one-dimensional Gross-Pitaevskii equation
Electronic Journal of Differential Equations, 2014 We establish a well-posedness result for the hydrodynamical form (HGP) of the one dimensional Gross-Pitaevskii equation (GP) via the classical form of this equation.
Haidar Mohamad
doaj
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.
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Order Parameter at the Boundary of a Trapped Bose Gas
, 1996 Through a suitable expansion of the Gross-Pitaevskii equation near the classical turning point, we obtain an explicit solution for the order parameter at the boundary of a trapped Bose gas interacting with repulsive forces.
A. Griffin +12 more
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The stochastic Gross-Pitaevskii equation
, 2001 We show how to adapt the ideas of local energy and momentum conservation in order to derive modifications to the Gross-Pitaevskii equation which can be used phenomenologically to describe irreversible effects in a Bose-Einstein condensate. Our approach involves the derivation of a simplified quantum kinetic theory, in which all processes are treated ...
Anglin, C. W. Gardiner J. R. +1 more
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Physical Review Research, 2020 We propose a superfluid phase of “many-fracton system” in which charge and total dipole moments are conserved quantities. In this work, both microscopic model and long-wavelength effective theory are analyzed. We start with a second quantized microscopic
Jian-Keng Yuan, Shuai A. Chen, Peng Ye
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