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An open source MATLAB program for fast numerical Feynman integral calculations for open quantum system dynamics on GPUs

Nikesh S. Dattani
Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, Oxford, OX1 3QZ, UK
arXiv:1205.6872v1 [quant-ph], 31 May 2012

@article{2012arXiv1205.6872D,

   author={Dattani}, N.~S.},

   title={"{An open source MATLAB program for fast numerical Feynman integral calculations for open quantum system dynamics on GPUs}"},

   journal={ArXiv e-prints},

   archivePrefix={"arXiv"},

   eprint={1205.6872},

   primaryClass={"quant-ph"},

   keywords={Quantum Physics, Mathematical Physics, Physics – Chemical Physics, Physics – Computational Physics},

   year={2012},

   month={may},

   adsurl={http://adsabs.harvard.edu/abs/2012arXiv1205.6872D},

   adsnote={Provided by the SAO/NASA Astrophysics Data System}

}

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This MATLAB program calculates the dynamics of the reduced density matrix of an open quantum system modeled by the Feynman-Vernon model. The user gives the program a vector describing the coordinate of an open quantum system, a hamiltonian matrix describing its energy, and a spectral distribution function and temperature describing the environment’s influence on it, in addition to the open quantum system’s intial density matrix and a grid of times. With this, the program returns the reduced density matrix of the open quantum system at all (or some) moments specified by that grid of times. This overall calculation can be divided into two stages: the setup of the Feynman integral, and the actual calculation of the Feynman integral for time-propagation of the density matrix. When this program calculates this propagation on a multi-core CPU, it is this propagation that is usually the rate limiting step of the calculation, but when it is calculated on a GPU, the propagation is calculated so quickly that the setup of the Feynman integal actually becomes the rate limiting step for most cases tested so far. The overhead of transfrring information from the CPU to the GPU and back seems to have negligible effect on the overall runtime of the program. When the required information cannot fit on the GPU, the user can choose to run the entire program on a CPU.
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