Mixing quantum and classical mechanics

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 56, Issue 1, 1997, Pages 162-175

  Prezhdo, Oleg V ^a   Kisil, Vladimir V ^b  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^b ODESSA NATIONAL UNIVERSITY   (Ukraine)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000176072     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.56.162     Document Type: Article

References (75)

1. J. Maddox, Nature (London) 373, 469 (1995).NATUAS
2. A. Anderson, Phys. Rev. Lett. 74, 621 (1995).PRLTAO
3. K. R. W. Jones, Phys. Rev. Lett. 76, 4087 (1996).PRLTAO
4. L. Diósi, Phys. Rev. Lett. 76, 4088 (1996).PRLTAO
5. I. R. Senitzky, Phys. Rev. Lett. 76, 4089 (1996).PRLTAO
6. A. Anderson, Phys. Rev. Lett. 76, 4090 (1996).PRLTAO
7. A. Anderson, LANL Report No. (unpublished).
8. L. L. Salcedo, LANL Report No. (unpublished).
9. L. Diósi, LANL e-print archive No. (unpublished).
10. L. Diósi, Quantum Semiclass. Opt. 8, 309 (1996).QUSOEC
11. D. Page, in Proceedings of the 5th Canandian Conference on General Relativity and Relativistic Astrophysics, edited by R. B. Mann and R. G. McLenaghan (Academic Press, Singapore, 1994).
12. W. Boucher and J. Traschen, Phys. Rev. D 37, 3522 (1988).PRVDAQ
13. A. Chamseddine and A. Connes, LANL Report No. (unpublished).
14. D. J. Diestler, J. Chem. Phys. 78, 2240 (1983).JCPSA6
15. I. V. Aleksandrov, Z. Naturforsch. 36A, 902 (1981).ZNTFA2
16. W. H. Miller, Adv. Chem. Phys. 25, 69 (1974).ADCPAA
17. W. H. Miller, Adv. Chem. Phys. 30, 77 (1975).ADCPAA
18. H. D. Meyer and W. H. Miller, J. Chem. Phys. 72, 2272 (1980).JCPSA6
19. J. C. Tully, in Dymanics of Molecular Collisions, edited by W. H. Miller (Plenum, New York, 1976), p. 217.
20. P. Pechukas, Phys. Rev. 181, 166 (1969).PHRVAO
21. P. Pechukas, Phys. Rev. 181, 174 (1969).PHRVAO
22. J. C. Tully, Catal. Lett. 9, 205 (1991).CALEER
23. S. Hammes-Schiffer and J. C. Tully, J. Chem. Phys. 101, 4657 (1994).JCPSA6
24. B. Space and D. F. Coker, J. Chem. Phys. 96, 652 (1992).JCPSA6
25. F. A. Webster, P. J. Rossky, and R. A. Friesner, Comput. Phys. Commun. 63, 494 (1991).CPHCBZ
26. P. J. Rossky and J. D. Simon, Nature (London) 370, 263 (1994).NATUAS
27. B. J. Schwartz, E. R. Bittner, O. V. Prezhdo, and P. J. Rossky, J. Chem. Phys. 104, 5942 (1996).JCPSA6
28. P. Ehrenfest, Z. Phys. 45, 455 (1927).ZEPYAA
29. K. Hepp, Commun. Math. Phys. 35, 265 (1974).CMPHAY
30. N. F. Mott, Proc. Camb. Philos. Soc. 27, 553 (1931).PCPSA4
31. M. H. Mittelman, Phys. Rev. 122, 449 (1961).PHRVAO
32. J. B. Delos, W. R. Thorson, and S. K. Knudson, Phys. Rev. A 6, 709 (1972).PLRAAN
33. J. B. Delos and W. R. Thorson, Phys. Rev. A 6, 720 (1972).PLRAAN
34. J. C. Tully and R. K. Preston, J. Chem. Phys. 55, 562 (1971).JCPSA6
35. J. C. Tully, J. Chem. Phys. 93, 1061 (1990).JCPSA6
36. O. V. Prezhdo and P. J. Rossky, J. Chem. Phys. (to be published).
37. R. Omnès, Rev. Mod. Phys. 64, 339 (1992).RMPHAT
38. W. H. Zurek, Prog. Theor. Phys. 89, 281 (1993).PTPKAV
39. L. Diósi, N. Gisin, J. Halliwell, and I. Percival, Phys. Rev. Lett. 74, 203 (1995).PRLTAO
40. G. C. Ghirardi, P. Pearle, and A. Rimini, Phys. Rev. A 42, 78 (1990).PLRAAN
41. O. V. Prezhdo (unpublished).
42. V. V. Kisil, J. Natur. Geom. 9, 1 (1996); LANL Report No. func-an/9405002 (unpublished).
43. V. V. Kisil, LANL Report No. fuct-an/9410001 (unpublished).
44. J. Dixmier, (Formula presented)-algebres et Leurs Representations (Gauthier-Villars, Paris, 1964).
45. J. Dauns and K. H. Hofmann, Representation of Rings by Sections, Memoirs of the American Mathematical Society Vol. 83 (AMS, Providence, RI, 1968).
46. K. H. Hofmann, Bull. Am. Math. Soc. 78, 291 (1972).BAMOAD
47. G. B. Folland, Harmonic Analysis in Phase Space (Princeton Univ. Press, Princeton, NJ, 1989).
48. A. A. Kirillov, Elements of the Theory of Representations (Springer-Verlag, New York, 1976).
49. V. I. Tatarskii, Usp. Fiz. Nauk 139, 587 (1983) [Sov. Phys. Usp. 26, 311 (1983)].SOPUAP
50. F. A. Berezin, Math. USSR-Izv. 8, 1109 (1974).
51. F. A. Berezin, Math. USSR-Izv. 9, 341 (1975).
52. C. A. Berger and L. A. Coburn, Trans. Am. Math. Soc. 301, 813 (1987).
53. L. A. Coburn, Proc. Symp. Pure Math. 51, 97 (1990).
54. L. A. Coburn, Algebraic Methods in Operator Theory (Birkhäuser-Verlag, New York, 1994), pp. 101–108.
55. L. A. Coburn and J. Xia, Commun. Math. Phys. 168, 23 (1995).CMPHAY
56. V. Guillemin, Integral Equations Operator Theory 7, 145 (1984).
57. V. Bargmann, Commun. Pure Appl. Math. 3, 215 (1961).CPAMAT
58. I. E. Segal, Lectures at the Summer Seminar on Applied Mathematics (American Mathematical Society, Providence, RI, 1963).
59. V. Fock, Z. Phys. 75, 622 (1932).ZEPYAA
60. R. Howe, J. Funct. Anal. 38, 188 (1980).JFUAAW
61. M. E. Taylor, Noncommutative Harmonic Analysis, Math. Survey and Monographs Vol. 22 (American Mathematical Society, Providence, RI, 1986).
62. V. I. Arnold, Mathematical Methods of Classic Mechanics (Springer-Verlag, Berlin, 1991).
63. M. P. Allen and D. J. Tildesley, Computer Simulations in Liquids (Oxford University Press, Oxford, Great Britain, 1990).
64. Computer Simulations in Chemical Physics, edited by M. P. Allen and D. J. Tildesley (Kluwer Academic Publishers, Dordrecht, Netherlands, 1993).
65. A. Szabo and N. S. Ostlund, Modern Quantum Chemistry, 1st revised ed. (McGraw-Hill, New York, 1989).
66. N. Makri and W. H. Miller, J. Chem. Phys. 87, 3248 (1987).JCPSA6
67. R. Kosloff and A. D. Hammerich, Faraday Discuss. Chem. Soc. 91, 239 (1991).FDCSB7
68. G. Stock, J. Chem. Phys. 103, 2888 (1995).JCPSA6
69. D. Antoniou and S. D. Schwartz, J. Chem. Phys. 104, 3526 (1996).JCPSA6
70. O. V. Prezhdo (unpublished).
71. F. A. Berezin, The Method of Second Quantization (Nauka, Moscow, Russia, 1988), in Russian.
72. M. A. Shubin, Pseudodifferential Operators and Spectral Theory (Nauka, Moscow, Russia, 1978), in Russian.
73. V. V. Kisil, LANL Report No. (unpublished).
74. G. B. Folland, in Fourier Analysis: Analytic and Geometric Aspects, Lecture Notes in Pure and Applied Mathematics No. 157, edited by W. O. Bray, P. S. Milojević, and Časlav V. Stanojević (Marcel Dekker, Inc., New York, 1994), pp. 121–147.
75. F. Antonsen, LANL Report No. (unpublished).