Numerical Feynman integrals for density operator dynamics using master equation interpolants: faster convergence and significant reduction of computational cost

Details Numerical Feynman integrals for density operator dynamics using master equation interpolants: faster convergence and significant reduction of computational cost Numerical Feynman integrals for density operator dynamics using master equation interpolants: faster convergence and significant reduction of computational cost

2010-09-09

arxiv.org/abs/1009.1674v2

Physics

Computational Physics

5 pages, 4 figures. v2: no change in results, no change in figures, fixed formatting on page 3, some word changes, version of

Scientific paper

The Feynman integral is one of the most accurate methods for calculating density operator dynamics in open quantum systems. However, the number of time steps that can realistically be used is always limited, therefore one often obtains an approximation of the density operator at a sparse grid of points in time. Instead of relying only on \textit{ad hoc} interpolation methods such as splines to estimate the system density operator in between these points, I propose a method that uses physical information to assist with this interpolation. This method is tested on a physically significant system, on which its use allows important qualitative features of the density operator dynamics to be captured with as little as 2 time steps in the Feynman integral. This method allows for an enormous reduction in the amount of memory and CPU time required for approximating density operator dynamics within a desired accuracy. Since this method does not change the way the Feynman integral itself is calculated, the value of the density operator approximation at the points in time used to discretize the Feynamn integral will be the same whether or not this method is used, but its approximation in between these points in time is considerably improved by this method.

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