Fourth-order algorithms for solving the imaginary-time Gross-Pitaevskii equation in a rotating anisotropic trap.
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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 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.
Phys Rev E Stat Nonlin Soft Matter Phys
author list (cited authors)
Chin, S. A., & Krotscheck, E.
complete list of authors
Chin, Siu A||Krotscheck, Eckhard