Fourth-Order Algorithms for Solving the Imaginary Time Gross-Pitaevskii Equation in a Rotating Anisotropic Trap

Details Fourth-Order Algorithms for Solving the Imaginary Time Gross-Pitaevskii Equation in a Rotating Anisotropic Trap Fourth-Order Algorithms for Solving the Imaginary Time Gross-Pitaevskii Equation in a Rotating Anisotropic Trap

2005-04-11

arxiv.org/abs/cond-mat/0504270v3

S. A. Chin and E. Krotscheck, Phys. Rev. E 72, 036705 (2005)

Physics

Condensed Matter

Statistical Mechanics

14 pages with 3 figures, revised figures with the use of the Lambert W-function for doing the self-consistent iterations. Publ

Scientific paper

10.1103/PhysRevE.72.036705

By implementing the exact density matrix for the rotating anisotropic harmonic trap, we derive a class of very fast and accurate fourth order algorithms for evolving the Gross-Pitaevskii equation in imaginary time. Such fourth order algorithms are possible only with the use of {\it forward}, positive time step factorization schemes. These fourth order algorithms converge at time-step sizes an order-of-magnitude larger than conventional second order algorithms. Our use of time-dependent factorization schemes provides a systematic way of devising algorithms for solving this type of nonlinear equations.

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