2014/11/11 by Philipp Bader, Bader, Philipp
Computer Science · Mathematics · Physics and Astronomy · #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations #Quantum Information and Cryptography #Spectroscopy and Quantum Chemical Studies
paper · pdf · doi:10.48550/arxiv.1411.2905
openalex publication_date 2014/11/11 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28
We present a new method to propagate rotating Bose-Einstein condensates\nsubject to explicitly time-dependent trapping potentials. Using algebraic\ntechniques, we combine Magnus expansions and splitting methods to yield any\norder methods for the multivariate and nonautonomous quadratic part of the\nHamiltonian that can be computed using only Fourier transforms at the cost of\nsolving a small system of polynomial equations. The resulting scheme solves the\nchallenging component of the (nonlinear) Hamiltonian and can be combined with\noptimized splitting methods to yield efficient algorithms for rotating\nBose-Einstein condensates. The method is particularly efficient for potentials\nthat can be regarded as perturbed rotating and trapped condensates, e.g., for\nsmall nonlinearities, since it retains the near-integrable structure of the\nproblem. For large nonlinearities, the method remains highly efficient if\nhigher order p > 2 is sought. Furthermore, we show how it can adapted to the\npresence of dissipation terms. Numerical examples illustrate the performance of\nthe scheme.\n