Mathematics – Numerical Analysis
Scientific paper
2010-07-20
Phys. Rev. E 83, 046711 (2011)
Mathematics
Numerical Analysis
12 pages of RevTex4-1, 8 figures; substantially revised and extended version
Scientific paper
10.1103/PhysRevE.83.046711
We consider the numerical integration of the Gross-Pitaevskii equation with a potential trap given by a time-dependent harmonic potential or a small perturbation thereof. Splitting methods are frequently used with Fourier techniques since the system can be split into the kinetic and remaining part, and each part can be solved efficiently using Fast Fourier Transforms. To split the system into the quantum harmonic oscillator problem and the remaining part allows to get higher accuracies in many cases, but it requires to change between Hermite basis functions and the coordinate space, and this is not efficient for time-dependent frequencies or strong nonlinearities. We show how to build new methods which combine the advantages of using Fourier methods while solving the timedependent harmonic oscillator exactly (or with a high accuracy by using a Magnus integrator and an appropriate decomposition).
Bader Philipp
Blanes Sergio
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