SPEEDUP Code for Calculation of Transition Amplitudes via the Effective Action Approach

Details SPEEDUP Code for Calculation of Transition Amplitudes via the Effective Action Approach SPEEDUP Code for Calculation of Transition Amplitudes via the Effective Action Approach

2011-05-03

arxiv.org/abs/1105.0542v1

Commun. Comput. Phys. 11 (2012) 739

Physics

Condensed Matter

Statistical Mechanics

17 pages, 3 figures, uses cicp.cls

Scientific paper

10.4208/cicp.131210.180411a

We present Path Integral Monte Carlo C code for calculation of quantum mechanical transition amplitudes for 1D models. The SPEEDUP C code is based on the use of higher-order short-time effective actions and implemented to the maximal order $p$=18 in the time of propagation (Monte Carlo time step), which substantially improves the convergence of discretized amplitudes to their exact continuum values. Symbolic derivation of higher-order effective actions is implemented in SPEEDUP Mathematica codes, using the recursive Schroedinger equation approach. In addition to the general 1D quantum theory, developed Mathematica codes are capable of calculating effective actions for specific models, for general 2D and 3D potentials, as well as for a general many-body theory in arbitrary number of spatial dimensions.

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