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Path Integral Monte Carlo

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Part of the book series: NATO ASI Series ((ASIC,volume 125))

Abstract

Path Integral Monte Carlo (PIMC) is one way of exploiting the connection between the diffusion equation and the Schrödinger equation for numerical computation based on sampling for quantum statistical mechanics. Starting from the introduction of the Wiener integral, that is the mathematical foundation supporting the numerical work, a number of methodological aspects of the implementation of PIMC are discussed, including suitable approximations to treat hard core particles, schemes for the calculation of free energy differences and of time dependent properties, and the problem of correlation and variance in the mean of estimators in Monte Carlo chains.

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References

  1. Fosdick, L. D.: 1962, J. Math. Phys. 3, p. 1251;

    Article  MathSciNet  ADS  MATH  Google Scholar 

  2. Fosdick, L. D. and Jordan, H. F.: 1966, Phys. Rev. 143, p. 58.

    Article  ADS  Google Scholar 

  3. Fosdick, L. D. and Jordan, H. F.: 1968, Phys. Rev. 171, p. 128.

    Article  ADS  Google Scholar 

  4. Fosdick, L. D. and Jacobson, R. C.: 1971, J. Compt. Phys. 1, p. 157.

    Article  ADS  Google Scholar 

  5. Lawande, S. V., Jensen, C. A., Sahlin, H. L.: 1969, J. Compt. Phys. 3, p. 416.

    Article  MathSciNet  ADS  Google Scholar 

  6. Lawande, S. V., Jensen, C. A., Sahlin, H. L.: 1979, 4, J. Compt. Phys. 4, p. 451.

    Article  ADS  Google Scholar 

  7. Lawande, S. V., Jensen, C. A., Sahlin, H. L.: 1971, J. Chem. Phys. 54, p. 445.

    Article  ADS  Google Scholar 

  8. Morita, T.: 1973, J. Phys. Soc. Jpn. 35, p. 98.

    Article  Google Scholar 

  9. Zamalin, V. M. and Norman, G. E.: 1973, U.S.S.R. Compt. Math. Phys. 13 (2), p. 169.

    Article  Google Scholar 

  10. Creutz, M. and Freedman, B.: 1981, Annals of Physics 132, p. 417.

    Article  MathSciNet  ADS  Google Scholar 

  11. Chandler, D. and Wolynes, P. G.: 1981, J. Chem. Phys. 74, p. 7.

    Article  Google Scholar 

  12. Schweitzer, K. S., Stratt, R. M., Chandler, D. and Wolynes, P. G.: 1981, J. Chem. Phys. 75, p. 3.

    Google Scholar 

  13. Frenkel, D. and Jacucci, G.: 1974, Rapporte d’Activite scientifique du CECAM, Orsay, France.

    Google Scholar 

  14. Jacucci, G. and Omerti, E., in print, J. Chem. Phys.

    Google Scholar 

  15. Kalos, M. H.: 1970, Phys. Rev. A2, p. 250

    ADS  Google Scholar 

  16. Kalos, M. H., D. Levesque and L. Verlet: 1974, Phys. Rev. A9, p. 2178.

    ADS  Google Scholar 

  17. Whitlock, P. A., M. H. Kalos: 1979, J. Comp. Phys. 30, p. 361.

    Article  MathSciNet  ADS  Google Scholar 

  18. Larsen, S. Y.: 1968, J. Chem. Phys. 48, p. 4.

    Article  Google Scholar 

  19. Barker, J.: 1979, J. Chem. Phys. 70, p. 2914.

    Article  ADS  Google Scholar 

  20. Uhlenbeck, G. E. and Beth, E.: 1936, Physica 3, p. 729.

    Article  MATH  Google Scholar 

  21. Lieb, E. H.: 1967, J. Math. Phys. 8, p. 43.

    Article  ADS  Google Scholar 

  22. Jacucci, G. and Rahman, A., “Comparing the Efficiency of Metropolis Monte Carlo and Molecular Dynamics Methods for Configuration Space Sampling,” submitted to J. Chem. Phys.

    Google Scholar 

  23. Valleau, J. P., Torrie, G. M.: 1977, “Modem Theoretical Chemistry” Vol. 5, Ed. Berne B. J. (Plenum) Chapter 5 and references therein.

    Google Scholar 

  24. Bennett, C. H.: 1975, “Exact Defect Calculations in Model Substances,” IBM Research Report RC4648 December 1973. Published in “Diffusion in Solids,” Eds. Nowick, A. S. and Burton, J. J., Academic Press, Inc., 1975.

    Google Scholar 

  25. Bennett, C. H.: 1976, J. Compt. Phys. 22, p. 245.

    Article  ADS  Google Scholar 

  26. Jacucci, G., Quirke, N., “Free Energy Calculations for Crystals” in “Computer simulation in the Physics and Chemistry of Solids,” Eds. Catlow, C. R. A., Mackrodt, W. C. and Saunders, V. R., Lecture Notes in Physics (Springer 1982); and 1980, Molec. Phys. 40, p. 1005.

    Google Scholar 

  27. Jacucci, G., Ronchetti, M.: 1980, Solid State Comm. 33, p. 35.

    Article  ADS  Google Scholar 

  28. Levy, P.: 1954, Le Mouvement Brownian, Memor. Sci. Math. Fasc. 126 (Gauthier-Villars, Paris).

    Google Scholar 

  29. Rahman, A. and Jacucci, G., “Relative Stability of FCC and BCC Structures for Model Systems at High Temperatures,” submitted to J. Chem. Phys.

    Google Scholar 

  30. Jacucci, G., Omerti, E. and Ronchetti, M., “A Quantum Statistical Monte Carlo Method for Free Energy Differences: Overlapping Distributions with Path Integrals,” submitted to Nuovo Cimento B.

    Google Scholar 

  31. McDonald, I. R., Singer, K.: 1967, Discuss. Faraday Soc. 43, p. 40; 1967, J. Chem. Phys. 4, p. 4766, ibid 50, p. 2308.

    Article  Google Scholar 

  32. Doniach, S. and Sondheimer, E. H.: 1974, “Green’s Functions for Solid State Physicists,” Benjamin (Reading, Massachusetts).

    Google Scholar 

  33. Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, E. and Teller, E.: 1953, J. Chem. Phys. 21, p. 1087.

    Article  ADS  Google Scholar 

  34. Herman, M. F., Bruskin, E. J., Berne, B. J.: 1982, J. Chem. Phys. 76, p. 5150.

    Article  ADS  Google Scholar 

  35. Giansanti, A. and Jacucci, G., “Variance and Correlation Length of Energy Estimators in Metropolis Path Integral Monte Carlo,” submitted to J. Chem. Phys.

    Google Scholar 

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© 1984 D. Reidel Publishing Company, Dordrecht, Holland

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Jacucci, G. (1984). Path Integral Monte Carlo. In: Kalos, M.H. (eds) Monte Carlo Methods in Quantum Problems. NATO ASI Series, vol 125. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-6384-9_10

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  • DOI: https://doi.org/10.1007/978-94-009-6384-9_10

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-009-6386-3

  • Online ISBN: 978-94-009-6384-9

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