Bose{endash}Einstein condensation in an external potential at zero temperature: Solitary-wave theory

Journal Article · Mon Nov 01 04:00:00 EST 1999 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.533043· OSTI ID:692551

Margetis, D ^[1]

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1. Gordon McKay Laboratory, Harvard University, Cambridge, Massachusetts 02138-2901 (United States)

For a trapped, dilute atomic gas of short-range, repulsive interactions at extremely low temperatures, when Bose{endash}Einstein condensation is nearly complete, some special forms of the time-dependent condensate wave function and the pair-excitation function, the latter being responsible for phonon creation, are investigated. Specifically, (i) a class of external potentials V{sub e}({bold r},t) that allow for localized, shape-preserving solutions to the nonlinear Schr{umlt o}dinger equation for the condensate wave function, each recognized as a solitary wave moving along an arbitrary trajectory, is derived and analyzed in any number of space dimensions; and (ii) for any such external potential and condensate wave function, the nonlinear integro-differential equation for the pair-excitation function is shown to admit solutions of the same nature. Approximate analytical results are presented for a sufficiently slowly varying trapping potential. Numerical results are obtained for the condensate wave function when V{sub e} is a time-independent, spherically symmetric harmonic potential. {copyright} {ital 1999 American Institute of Physics.}

• OSTI ID: 692551
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 11 Vol. 40; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
BOSE-EINSTEIN CONDENSATION
POTENTIALS
SCHROEDINGER EQUATION
SOLITONS
TRAPPING
WAVE FUNCTIONS