Reconstruction of thermally symmetrized quantum autocorrelation functions from imaginary-time data

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 70, Issue 6 2, 2004, Pages

  Predescu, Cristian ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; CORRELATION METHODS; ERROR DETECTION; FUNCTIONS; INFORMATION RETRIEVAL; LAPLACE TRANSFORMS; MONTE CARLO METHODS; POLYNOMIAL APPROXIMATION; PROBLEM SOLVING; THEOREM PROVING;

IMAGINARY-TIME DATA; INPUT DATA; QUANTUM AUTOCORRELATION; SYMMETRIC ECKART BARRIER;

QUANTUM THEORY;

EID: 41349116282     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.70.066705     Document Type: Article

References (69)

1. R. P. Feynman, Rev. Mod. Phys. 20, 367 (1948).
2. A. M. Amini and M. F. Herman, J. Chem. Phys. 99, 5087 (1993).
3. B. J. Berne and D. Thirumalai, Annu. Rev. Phys. Chem. 47, 401 (1986).
4. R. H. Cameron, J. Math. Phys. 39, 126 (1960).
5. J. D. Doll, J. Chem. Phys. 81, 3536 (1984).
6. V. S. Filinov, Nucl. Phys. B 271, 717 (1986).
7. N. Makri and W. H. Miller, Chem. Phys. Lett. 139, 10 (1987).
8. J. D. Doll, T. L. Beck, and D. L. Freeman, J. Chem. Phys. 89, 5753 (1988).
9. C. H. Mak, Phys. Rev. Lett. 68, 899 (1992).
10. G. Baym and D. Mermin, J. Math. Phys. 2, 232 (1961).
11. E. Nelson, J. Math. Phys. 5, 332 (1964).
12. H.-B. Schüttler and D. J. Scalapino, Phys. Rev. Lett. 55, 1204 (1985).
13. S. R. White, D. J. Scalapino, R. L. Sugar, and N. E. Bickers, Phys. Rev. Lett. 63, 1523 (1989).
14. M. Jarrell and O. Biham, Phys. Rev. Lett. 63, 2504 (1989).
15. M. Jarrell and J. E. Gubernatis, Phys. Rep. 269, 133 (1996).
16. J. E. Gubernatis, M. Jarrell, R. N. Silver, and D. S. Sivia, Phys. Rev. B 44, 6011 (1991).
17. D. Thirumalai and B. J. Berne, J. Chem. Phys. 79, 5029 (1983).
18. E. Gallicchio and B. J. Berne, J. Chem. Phys. 101, 9909 (1994).
19. D. Kim, J. D. Doll, and J. E. Gubernatis, J. Chem. Phys. 106, 1641 (1997).
20. D. Kim, J. D. Doll, and D. L. Freeman, J. Chem. Phys. 108, 3871 (1998).
21. G. Krilov, E. Sim, and B. J. Berne, J. Chem. Phys. 114, 1075 (2001).
22. W. H. Miller, S. D. Schwartz, and J. W. Tromp, J. Chem. Phys. 79, 4889 (1983).
23. E. Rabani, G. Krilov, and B. J. Berne, J. Chem. Phys. 112, 2605 (2000).
24. E. Sim, G. Krilov, and B. J. Berne, J. Phys. Chem. A 105, 2824 (2001).
25. E. Rabani, D. R. Reichman, G. Krilov, and B. J. Berne, Proc. Natl. Acad. Sci. U.S.A. 99, 1129 (2002).
26. S. R. White, Phys. Rev. B 44, 4670 (1991).
27. S. R. White, Phys. Rev. B 46, 5678 (1992).
28. M. Caffarel and D. M. Ceperley, J. Chem. Phys. 97, 8415 (1992).
29. J. Deisz, K.-H. Luk, M. Jarrell, and D. L. Cox, Phys. Rev. B 46, 3410 (1992).
30. J. Deisz, M. Jarrell, and D. L. Cox, Phys. Rev. B 48, 10227 (1993).
31. J. Skilling, in Maximum Entropy and Bayesian Methods, edited by J. Skilling (Kluwer, Dordrecht, 1989), p. 455.
32. R. N. Silver and H. Röder, Int. J. Mod. Phys. C 5, 735 (1994).
33. D. A. Drabold and O. F. Sankey, Phys. Rev. Lett. 70, 3631 (1993).
34. L. W. Wang, Phys. Rev. B 49, 10154 (1994).
35. R. N. Silver, H. Röder, A. F. Voter, and J. D. Kress, J. Comput. Phys. 124, 115 (1996).
36. R. N. Silver and H. Röder, Phys. Rev. E 56, 4822 (1997).
37. W. H. Miller, J. Chem. Phys. 61, 1823 (1974).
38. W. H. Miller, J. Phys. Chem. A 102, 793 (1998).
39. G. A. Athanassoulis and P. N. Gavriliadis, Probab. Eng. Mech. 17, 273 (2002).
40. E. T. Jaynes, Phys. Rev. 106, 620 (1957).
41. A. Tagliani, J. Math. Phys. 35, 5087 (1994).
42. C. Predescu and J. D. Doll, J. Chem. Phys. 117, 7448 (2002).
43. C. Predescu, D. Sabo, J. D. Doll, and D. L. Freeman, J. Chem. Phys. 119, 12119 (2003).
44. J. N. Lyness, Math. Comput. 22, 352 (1968).
45. J. D. Doll, M. Eleftheriou, S. A. Corcelli, and David L. Freeman, Quantum Monte Carlo Methods in Physics and Chemistry, edited by M. P. Nightingale and C. J. Umrigar, Vol. X of NATO Advanced Study Institute Series, Series C: Mathematical and Physical Sciences (Kluwer, Dordrecht, 1999).
46. B. J. Berne and G. D. Harp, Adv. Chem. Phys. 17, 63 (1970).
47. H. Hamburger, Math. Ann. 81, 235 (1920); 82, 120 (1921); 82, 168 (1921).
48. H. Hamburger, Math. Ann. 81, 235 (1920); 82, 120 (1921); 82, 168 (1921).
49. H. Hamburger, Math. Ann. 81, 235 (1920); 82, 120 (1921); 82, 168 (1921).
50. R. Durrett, Probability: Theory and Examples, 2nd ed. (Duxbury, New York, 1996).
51. B. Simon, Functional Integration and Quantum Physics (Academic, London, 1979).
52. J. Barker, J. Chem. Phys. 70, 2914 (1979).
53. M. F. Herman, E. J. Bruskin, and B. J. Berne, J. Chem. Phys. 76, 5150 (1982).
54. R. Paley, N. Wiener, and A. Zygmund, Math. Z. 37, 647 (1933).
55. C. Predescu, D. Sabo, J. D. Doll, and D. L. Freeman, J. Chem. Phys. 119, 10475 (2003).
56. A. D. Klemm and R. G. Storer, Aust. J. Phys. 26, 43 (1973).
57. D. Thirumalai, E. J. Bruskin, and B. J. Berne, J. Chem. Phys. 79, 5063 (1983).
58. T. Yamamoto and W. H. Miller, J. Chem. Phys. 120, 3086 (2004).
59. E. T. Jaynes, in The Maximum Entropy Formalism, edited by R. D. Levine and M. Tribus (MIT Press, Cambridge, 1978), pp. 15-118.
60. J. Skilling, in Maximum Entropy and Bayesian Methods edited by J. Skilling (Kluwer, Dordrecht, 1989), p. 45.
61. S. F. Gull, in Maximum Entropy and Bayesian Methods (Ref. [58]), p. 53.
62. A. Tagliani, J. Comput. Appl. Math. 90, 157 (1998).
63. W. H. Miller, Y. Zhao, M. Ceotto, and S. Yang, J. Chem. Phys. 119, 1329 (2003).
64. Y. Hida, X. S. Li, and D. H. Bailey, in Proceedings of the 15th IEEE Symposium on Computer Arithmetic (IEEE Computer Society, Englewood Cliffs, NJ, 2001), pp. 155-162.
65. N. F. Hansen and H. C. Andersen, J. Chem. Phys. 101, 6032 (1994).
66. I. R. Khan and R. Ohba, J. Comput. Appl. Math. 107, 179 (1999).
67. C. Predescu, Phys. Rev. E 69, 056701 (2004).
68. C. J. Geyer, in Computing Science and Statistics: Proceedings of the 23rd Symposium on the Interface, edited by E. M. Keramigas (Interface Foundation, Fairfax, 1991), pp. 156-163.
69. K. Hukushima and K. Nemoto, J. Phys. Soc. Jpn. 65, 1604 (1996).