Energy estimators for random series path-integral methods

Journal of Chemical Physics

Volumn 119, Issue 20, 2003, Pages 10475-10488

  Predescu, Cristian ^a   Sabo, Dubravko ^a   Doll, J D ^a   Freeman, D L ^b  

^a BROWN UNIVERSITY   (United States)

^b University of Rhode Island   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; HYDROGEN BONDS; MONTE CARLO METHODS; NUMERICAL METHODS; STATISTICAL MECHANICS;

MOLECULAR HYDROGEN CLUSTER; PATH INTEGRAL METHODS;

QUANTUM THEORY;

EID: 0348207661     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1619372     Document Type: Article

References (32)

1. Quantum Monte Carlo Methods in Physics and Chemistry, edited by M. P. Nightingale and C. J. Umrigar (Kluwer, Drodrecht, 1999).
2. C. Predescu and J. D. Doll, J. Chem. Phys. 117, 7448 (2002).
3. C. Predescu, J. D. Doll and D. L. Freeman, Asymptotic Convergence of the Partial Averaging Technique, e-print: http://arxiv.org/abs/cond-mat/0301525
4. C. Predescu, Reweighted Methods: Definition and Asymptotic Convergence, e-print: http://arXiv.org/abs/cond-mat/0302171
5. J. D. Doll, R. D. Coalson, and D. L. Freeman, Phys. Rev. Lett. 55, 1 (1985)
6. R. D. Coalson, D. L. Freeman, and J. D. Doll, J. Chem. Phys. 85, 4567 (1986).
7. C. Predescu, D. Sabo, and J. D. Doll, Numerical Implementation of Some Reweighted Path Integral Techniques, e-print: http://arXiv.org/abs/condmat/0305436
8. M. F. Ferman, E. J. Bruskin, and B. J. Berne, J. Chem. Phys. 76, 5051 (1982).
9. A. Giansanti and G. Jacucci, J. Chem. Phys. 89, 7454 (1988).
10. P. A. Fernandes, A. P. Carvalho, and J. P. P. Ramalho, J. Chem. Phys. 103, 5720 (1995).
11. J. Cao and B. J. Berne, J. Chem. Phys. 91, 6359 (1989).
12. M. Kolar and S. F. O'Shea, J. Phys. A 29, 3471 (1996).
13. W. Janke and T. Sauer, J. Chem. Phys. 107, 5821 (1997).
14. D. M. Ceperley, Rev. Mod. Phys. 67, 279 (1995).
15. K. R. Glaesemann and L. E. Fried, J. Chem. Phys. 116, 5951 (2002).
16. C. Chakravarty, M. C. Gordillo, and D. M. Ceperley, J. Chem. Phys. 109, 2123 (1998).
17. J. D. Doll and D. L. Freeman, J. Chem. Phys. 111, 7685 (1999).
18. B. Simon, Functional Integration and Quantum Physics (Academic, London, 1979).
19. R. Durrett, Probability: Theory and Examples, 2nd ed. (Duxbury, New York, 1996), pp. 430-431.
20. S. Kwapien and W. A. Woyczynski, Random Series and Stochastic Integrals: Single and Multiple (Birkhäuser, Boston, 1992), Theorem 2.5.1.
21. C. Predescu and J. D. Doll, Phys. Rev. E 67, 026124 (2003).
22. H. P. McKean, Jr., Stochastic Integrals (Academic, New York, 1969).
23. P. Sindzingre, D. M. Ceperley, and M. L. Klein, Phys. Rev. Lett. 67, 1871 (1991).
24. J. P. Neirotti, D.L. Freeman, and J. D. Doll, Phys. Rev. E 62, 7445 (2000).
25. N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. M. Teller, and E. Teller, J. Chem. Phys. 21, 1087 (1953).
26. M. Kalos and P. Whitlock, Monte Carlo Methods (Wiley-Interscience, New York, 1986).
27. M. Matsumoto and T. Nishimura, ACM Trans. Model. Comput. Simul. 8, 3 (1998).
28. M. Matsumoto and T. Nishimura, in Monte Carlo and Quasi-Monte Carlo Methods 1998 (Springer-Verlag, New York, 2000), pp. 56-69.
29. http://www.math.keio.ac.jp/~matumoto/emt.html
30. S. S. Shapiro and M. B. Wilk, Biometrika 52, 591 (1965).
31. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes (Cambridge University, Cambridge, 1992), Chap. 14.3.
32. J. P. Valleau and S. G. Whittington, in Statistical Mechanics, edited by B. J. Berne (Plenum, New York, 1977), Chap. 4, p. 145.