Bose-Einstein condensation dynamics in three dimensions by the pseudospectral and finite-difference methods

@article{Muruganandam2003BoseEinsteinCD,
  title={Bose-Einstein condensation dynamics in three dimensions by the pseudospectral and finite-difference methods},
  author={Paulsamy Muruganandam and Sadhan K. Adhikari},
  journal={Journal of Physics B},
  year={2003},
  volume={36},
  pages={2501-2513}
}
We suggest a pseudospectral method for solving the three-dimensional time-dependent Gross–Pitaevskii (GP) equation, and use it to study the resonance dynamics of a trapped Bose–Einstein condensate induced by a periodic variation in the atomic scattering length. When the frequency of oscillation of the scattering length is an even multiple of one of the trapping frequencies along the x, y or z direction, the corresponding size of the condensate executes resonant oscillation. Using the concept of… Expand

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References

SHOWING 1-10 OF 87 REFERENCES
Bose-Einstein condensation dynamics from the numerical solution of the Gross-Pitaevskii equation
We study certain stationary and time-evolution problems of trapped Bose-Einstein condensates using the numerical solution of the Gross-Pitaevskii (GP) equation with both spherical and axialExpand
Numerical solution of the Gross--Pitaevskii equation for Bose--Einstein condensation
We study the numerical solution of the time-dependent Gross-Pitaevskii equation (GPE) describing a Bose-Einstein condensate (BEC) at zero or very low temperature. In preparation for the numerics weExpand
Numerical study of the spherically symmetric gross-pitaevskii equation in two space dimensions
  • Adhikari
  • Physics, Medicine
  • Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 2000
We present a numerical study of the time-dependent and time-independent Gross-Pitaevskii (GP) equation in two space dimensions, which describes the Bose-Einstein condensate of trapped bosons atExpand
Numerical solution of the gross-pitaevskii equation using an explicit finite-difference scheme: An application to trapped bose-einstein condensates
TLDR
A fast, explicit time-marching scheme for the solution of the Gross-Pitaevskii equation in cylindrical geometry is presented and used to address the formation of matter-wave pulses that result from gravity-induced transport of a condensate in an optical potential. Expand
Numerical solution of the two-dimensional Gross-Pitaevskii equation for trapped interacting atoms
Abstract We present a numerical scheme for solving the time-independent nonlinear Gross–Pitaevskii equation in two dimensions describing the Bose–Einstein condensate of trapped interacting neutralExpand
Free expansion of Bose-Einstein condensates with quantized vortices
The expansion of Bose-Einstein condensates with quantized vortices is studied by solving numerically the time-dependent Gross-Pitaevskii equation at zero temperature. For a condensate initiallyExpand
Resonance in Bose-Einstein condensate oscillation from a periodic variation in scattering length
Using the explicit numerical solution of the axially symmetric Gross–Pitaevskii equation, we study the oscillation of the Bose–Einstein condensate (BEC) induced by a periodic variation in the atomicExpand
Theory of Bose-Einstein condensation in trapped gases
The phenomenon of Bose-Einstein condensation of dilute gases in traps is reviewed from a theoretical perspective. Mean-field theory provides a framework to understand the main features of theExpand
Numerical approach to the ground and excited states of a Bose-Einstein condensed gas confined in a completely anisotropic trap
The ground and excited states of a weakly interacting and dilute Bose-Einstein condensed gas, confined in a completely anisotropic harmonic oscillator potential, are determined at zero temperatureExpand
Mean-field description of collapsing and exploding Bose-Einstein condensates
We perform numerical simulations based on the time-dependent mean-field Gross-Pitaevskii equation to understand some aspects of a recent experiment by Donley et al. [Nature (London) 412, 295 (2001)]Expand
...
1
2
3
4
5
...