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

Published online by Cambridge University Press:  20 August 2015

Antun Balaž ,
Ivana Vidanović ,
Danica Stojiljković ,
Dušan Vudragović ,
Aleksandar Belić  and
Aleksandar Bogojević
Antun Balaž*
Affiliation:
Scientific Computing Laboratory, Institute of Physics Belgrade, University of Belgrade, Pregrevica 118, 11080 Belgrade, Serbia
Ivana Vidanović*
Affiliation:
Scientific Computing Laboratory, Institute of Physics Belgrade, University of Belgrade, Pregrevica 118, 11080 Belgrade, Serbia
Danica Stojiljković*
Affiliation:
Scientific Computing Laboratory, Institute of Physics Belgrade, University of Belgrade, Pregrevica 118, 11080 Belgrade, Serbia
Dušan Vudragović*
Affiliation:
Scientific Computing Laboratory, Institute of Physics Belgrade, University of Belgrade, Pregrevica 118, 11080 Belgrade, Serbia
Aleksandar Belić*
Affiliation:
Scientific Computing Laboratory, Institute of Physics Belgrade, University of Belgrade, Pregrevica 118, 11080 Belgrade, Serbia
Aleksandar Bogojević*
Affiliation:
Scientific Computing Laboratory, Institute of Physics Belgrade, University of Belgrade, Pregrevica 118, 11080 Belgrade, Serbia
*
Corresponding author.Email:antun@ipb.ac.rs
Email:ivanavi@ipb.ac.rs
Email:danica@ipb.ac.rs
Email:dusan@ipb.ac.rs
Email:abelic@ipb.ac.rs
Email:alex@ipb.ac.rs
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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 Schrödinger 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.

Keywords

81Q0581Q1565Y0465B99Transition amplitudeeffective actionpath integralsMonte Carlo
Type
Research Article
Information
Communications in Computational Physics , Volume 11 , Issue 3 , March 2012 , pp. 739 - 755
Copyright
Copyright © Global Science Press Limited 2012

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