Commun. Comput. Phys., 11 (2012), pp. 739-755.


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

Antun Balaz 1*, Ivana Vidanovic 1, Danica Stojiljkovic 1, Dusan Vudragovic 1, Aleksandar Belic 1, Aleksandar Bogojevic 1

1 Scientific Computing Laboratory, Institute of Physics Belgrade, University of Belgrade, Pregrevica 118, 11080 Belgrade, Serbia.

Received 13 December 2010; Accepted 18 April 2011
Available online 28 October 2011
doi:10.4208/cicp.131210.180411a

Abstract

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 Schrodinger 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.

AMS subject classifications: 81Q05, 81Q15, 65Y04, 65B99

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Key words: Transition amplitude, effective action, path integrals, Monte Carlo.

*Corresponding author.
Email: antun@ipb.ac.rs (A. Balaz), ivanavi@ipb.ac.rs (I. Vidanovic), danica@ipb.ac.rs (D. Stojiljkovic), dusan@ipb.ac.rs (D. Vudragovic), abelic@ipb.ac.rs (A. Belic), alex@ipb.ac.rs (A. Bogojevic)
 

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