Nonlinear dynamics of Bose-condensed gases by means of a q-Gaussian variational approach

Alexandru I. Nicolin and R. Carretero-González

Physica A: Statistical Mechanics and its Applications, 2008, vol. 387, issue 24, 6032-6044

Abstract: We propose a versatile variational method to investigate the spatio-temporal dynamics of one-dimensional magnetically-trapped Bose-condensed gases. To this end we employ a q-Gaussian trial wave-function that describes both the low- and the high-density limit of the ground state of a Bose-condensed gas. Unlike previous analytical models, we do not approximate the dynamics of the condensate as a dynamical rescaling of the initial density profile. Instead, we allow the shape of the condensate’s density profile to change in time. Our main result consists of reducing the Gross–Pitaevskii equation, a nonlinear partial differential equation describing the T=0 dynamics of the condensate, to a set of only three equations: two coupled nonlinear ordinary differential equations describing the phase and the curvature of the wave-function and a separate algebraic equation yielding the generalized width. Our equations recover those of the usual Gaussian variational approach (in the low-density regime), and the hydrodynamic equations that describe the high-density regime. Finally, we show a detailed comparison between the numerical results of our equations and those of the original Gross–Pitaevskii equation.

Date: 2008
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437108005797
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:387:y:2008:i:24:p:6032-6044

DOI: 10.1016/j.physa.2008.06.055

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().