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Volume 11, Issue 3
SPEEDUP Code for Calculation of Transition Amplitudes via the Effective Action Approach

Antun Balaž, Ivana Vidanović, Danica Stojiljković, Dušan Vudragović, Aleksandar Belić & Aleksandar Bogojević

DOI: 10.4208/cicp.131210.180411a

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

Published online: 2012-11

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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.

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COPYRIGHT: © Global Science Press

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@Article{CiCP-11-739, author = {Balaž , AntunVidanović , IvanaStojiljković , DanicaVudragović , DušanBelić , Aleksandar and Bogojević , Aleksandar}, title = {SPEEDUP Code for Calculation of Transition Amplitudes via the Effective Action Approach}, journal = {Communications in Computational Physics}, year = {2012}, volume = {11}, number = {3}, pages = {739--755}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.131210.180411a}, url = {http://global-sci.org/intro/article_detail/cicp/7389.html} }
TY - JOUR T1 - SPEEDUP Code for Calculation of Transition Amplitudes via the Effective Action Approach AU - Balaž , Antun AU - Vidanović , Ivana AU - Stojiljković , Danica AU - Vudragović , Dušan AU - Belić , Aleksandar AU - Bogojević , Aleksandar JO - Communications in Computational Physics VL - 3 SP - 739 EP - 755 PY - 2012 DA - 2012/11 SN - 11 DO - http://doi.org/10.4208/cicp.131210.180411a UR - https://global-sci.org/intro/article_detail/cicp/7389.html KW - AB -

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.

Balaž , AntunVidanović , IvanaStojiljković , DanicaVudragović , DušanBelić , Aleksandar and Bogojević , Aleksandar. (2012). SPEEDUP Code for Calculation of Transition Amplitudes via the Effective Action Approach. Communications in Computational Physics. 11 (3). 739-755. doi:10.4208/cicp.131210.180411a
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