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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:[email protected]
Email:[email protected]
Email:[email protected]
Email:[email protected]
Email:[email protected]
Email:[email protected]
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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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References

[1]Feynman, R. P., Rev. Mod. Phys. 20, 367 (1948).Google Scholar
[2]Feynman, R. P. and Hibbs, A. R., Quantum Mechanics and Path Integrals McGraw-Hill, New York, 1965).Google Scholar
[3]Kleinert, H., Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets, 5th ed. (World Scientific, Singapore, 2009).CrossRefGoogle Scholar
[4]Stojiljković, D., Bogojević, A., and Balaž, A., Phys. Lett. A 360, 205 (2006).CrossRefGoogle Scholar
[5]Bogojević, A., Vidanović, I., Balaž, A., and Belić, A., Phys. Lett. A 372, 3341 (2008).CrossRefGoogle Scholar
[6]Sethia, A., Sanyal, S., and Singh, Y., J. Chem. Phys. 93, 7268 (1990).Google Scholar
[7]Sethia, A., Sanyal, S., and Hirata, F., Chem. Phys. Lett. 315, 299 (1999).Google Scholar
[8]Vidanović, I., Bogojević, A., and Belić, A., Phys. Rev. E 80, 066705 (2009).Google Scholar
[9]Vidanović, I., Bogojević, A., Balaž, A., and Belić, A., Phys. Rev. E 80, 066706 (2009).CrossRefGoogle Scholar
[10]Balaž, A., Vidanović, I., Bogojević, A., and Pelster, A., Phys. Lett. A 374, 1539 (2010).CrossRefGoogle Scholar
[11]Feynman, R. P., Statistical Mechanics (W. A. Benjamin, New York, 1972).Google Scholar
[12]Parisi, G., Statistical Field Theory (Addison Wesley, New York, 1988).Google Scholar
[13]Bogojević, A., Balaž, A., and Belić, A., Phys. Rev. Lett. 94, 180403 (2005).CrossRefGoogle Scholar
[14]Bogojević, A., Balaž, A., and Belić, A., Phys. Rev. B 72, 064302 (2005).Google Scholar
[15]Bogojević, A., Balaž, A., and Belić, A., Phys. Lett. A 344, 84 (2005).CrossRefGoogle Scholar
[16]Bogojević, A., Balaž, A., and Belić, A., Phys. Rev. E 72, 036128 (2005).Google Scholar
[17]Balaž, A., Bogojević, A., Vidanović, I., and Pelster, A., Phys. Rev. E 79, 036701 (2009).Google Scholar
[18]Grujić, J., Bogojević, A., and Balaž, A., Phys. Lett. A 360, 217 (2006).Google Scholar
[19]SPEEDUP code distribution, http://www.scl.rs/speedup/Google Scholar
[20]Ceperley, D. M., Rev. Mod. Phys. 67, 279 (1995).Google Scholar
[21]Takahashi, M. and Imada, M., J. Phys. Soc. Jpn. 53, 3765 (1984).Google Scholar
[22]Li, X. P. and Broughton, J. Q., J. Chem. Phys. 86, 5094 (1987).CrossRefGoogle Scholar
[23]De, H. Raedt and De Raedt, B., Phys. Rev. A 28, 3575 (1983).Google Scholar
[24]Jang, S., Jang, S., and Voth, G., J. Chem. Phys. 115, 7832 (2001).Google Scholar
[25]Makri, N. and Miller, W. H., Chem. Phys. Lett. 151, 1 (1988);Google ScholarGoogle Scholar
[26]Makri, N., Chem. Phys. Lett. 193, 435 (1992).CrossRefGoogle Scholar
[27]Alford, M., Klassen, T. R., and Lepage, G. P., Phys. Rev. D 58, 034503 (1998).Google Scholar
[28]Chin, S. A. and Krotscheck, E., Phys. Rev. E 72, 036705 (2005).Google Scholar
[29]Hernández, E. R., Janecek, S., Kaczmarski, M., Krotscheck, E., Phys. Rev. B 75, 075108 (2007).CrossRefGoogle Scholar
[30]Ciftja, O. and Chin, S. A., Phys. Rev. B 68, 134510 (2003).CrossRefGoogle Scholar
[31]Sakkos, K., Casulleras, J., and Boronat, J., J. Chem. Phys. 130, 204109 (2009).CrossRefGoogle Scholar
[32]Janecek, S. and Krotscheck, E., Comput. Phys. Comm. 178, 835 (2008).Google Scholar
[33]Bandrauk, A. D. and Shen, H., J. Chem. Phys. 99, 1185 (1993).CrossRefGoogle Scholar
[34]Chin, S. A. and Chen, C. R., J. Chem. Phys. 117, 1409 (2002).Google Scholar
[35]Omelyan, I. P., Mryglod, I. M., and Folk, R., Comput. Phys. Commun. 151, 272 (2003).Google Scholar
[36]Goldstein, G. and Baye, D., Phys. Rev. E 70, 056703 (2004).CrossRefGoogle Scholar
[37]Chin, S. A., arXiv:0809.0914.Google Scholar
[38]Chin, S. A., Janecek, S., and Krotscheck, E., Comput. Phys. Comm. 180, 1700 (2009).Google Scholar
[39]Chin, S. A., Janecek, S., and Krotscheck, E., Chem. Phys. Lett. 470, 342 (2009).Google Scholar
[40]Mathematica software package, http://www.wolfram.com/mathematica/Google Scholar
[41]Math Tensor package, http://smc.vnet.net/mathtensor.htmlGoogle Scholar
[42]Scalable Parallel Random Number Generator library, http://sprng.fsu.edu/Google Scholar