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Numerical method for evolving the projected Gross-Pitaevskii equation

Jack Dodd Centre for Quantum Technology, Department of Physics, University of Otago, Dunedin, New Zealand

Phys. Rev. E 78, 026704 – Published 8 August, 2008

DOI: https://doi.org/10.1103/PhysRevE.78.026704

Abstract

In this paper we describe a method for evolving the projected Gross-Pitaevskii equation (PGPE) for a Bose gas in a harmonic oscillator potential. The central difficulty in solving this equation is the requirement that the classical field is restricted to a small set of prescribed modes that constitute the low energy classical region of the system. We present a scheme, using a Hermite-polynomial based spectral representation, that precisely implements this mode restriction and allows an efficient and accurate solution of the PGPE. We show equilibrium and nonequilibrium results from the application of the PGPE to an anisotropic trapped three-dimensional Bose gas.

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References (47)

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Numerical method for evolving the projected Gross-Pitaevskii equation

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