Phase space approach to dissipative molecular dynamics

Advances in Chemical Physics

Volumn 111, Issue , 2000, Pages 219-398

  Kohen, Daniela ^a,c   Tannor, David J ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b WEIZMANN INSTITUTE OF SCIENCE   (Israel)

^c SMITH COLLEGE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000501406     PISSN: 00652385     EISSN: None     Source Type: Book Series    
DOI: None     Document Type: Article

References (143)

1. P. Hänggi, P. Talkner, and M. Borkovec, Rev. Mod. Phys. 62, 251 (1990).
2. S. Arrhenius, Z. Phys. Chem. (Leipzig) 4, 226 (1889).
3. L. Farkas, Z. Phys. Chem. (Leipzig) 125, 236 (1927).
4. F. A. Lindemann, Trans. Faraday Soc. 17, 598 (1922).
5. C. N. Hinshelwood, in The Kinetics of Chemical Change in Caseous Sytems, Clarendon, Oxford, 1926;
6. C. N. Hinshelwood. Proc. R. Soc. London, Ser. A 1113, 230 (1926).
7. H. Eyring, J. Chem. Phys. 3, 107 (1935).
8. M. Polanyi and E. Wigner, Z. Phys. Chem. Abt. A 139, 439 (1928).
9. H. A. Kramers, Physica (Utrecht) 7, 284 (1940).
10. R. F. Grote and J. T. Hynes, J. Chem. Phys. 73, 2715 (1980).
11. S. H. Northrup and J. T. Hynes, J. Chem. Phys. 73, 2700 (1980).
12. P. Hänggi and F. Mojtabai, Phys. Rev. A 26, 1168 (1982).
13. E. Pollak, J. Chem. Phys. 85, 865 (1986).
14. E. Pollak, H. Grabert, and P. Hänggi, J. Chem. Phys. 91, 4073 (1989).
15. B. J. Berne (private communication, 19**).
16. B. J. Genner, K. R. Wilson, and J. T. Hynes, J. Chem. Phys. 90, 3537 (1989).
17. J. Bader and B. J. Berne (private communication),
18. a preliminary report of this derivation is contained in B. J. Berne, in Activated Barrier Theory (P. Hänggi and G. Fleming, eds.), World Scientific, 1993.
19. E. Pollak and P. Talkner, Phys. Rev. E 47, 922 (1993).
20. D. Chandler, J. Chem. Phys. 68, 2959 (1978).
21. D. Chandler, Introduction to Modern Statistical Mechanics, Oxford, New York, 1987.
22. L. Onsager, Phys. Rev. Lett. 37 405 (1931), part I;
23. Phys. Rev. Lett. 38 2265 (1931), part II.
24. E. P. Wigner, Ph.D. thesis, Technische Hochschule, Berlin (1925),
25. M. Polanyi and E. Wigner, Z. Phys. Chem. Abt. A 139, 439 (1928).
26. J. C. Keck, Adv. At. Mol. Phys. 8, 39 (1972).
27. H. S. Johnston, Gas Phase Reaction Rate Theory, Ronald, New York, 1966.
28. P. Pechukas and F. McLafferty, J. Chem. Phys. 58, 1622 (1972).
29. P. Pechukas, in Dynamics of Molecular Collisions, Part B (W. H. Miller, ed.), Plenum, New York, 1976, p. 269.
30. B. J. Berne, in Multiple Time Scales (J. U. Brackbill and B. I. Cohen, eds.), Academic, New York, 1985.
31. J. B. Anderson, J. Chem. Phys. 58, 4684 (1973).
32. C. H. Bennett, in Algorithms for Chemical Computation (R. E. Christofferson, eds.), American Chemical Society, Washington, D.C., 1977.
33. J. A. Montgomery, D. Chandler and B. J. Berne, J. Chem. Phys. 70, 4056 (1979).
34. E. P. Wigner, J. Chem. Phys. 5, 720 (1937).
35. J. C. Keck, J. Chem. Phys. 32, 1035 (1960);
36. Adv. Chem. Phys. 13, 85 (1967).
37. M. Borkovec and P. Talkner, J. Chem. Phys. 92, 5307 (1990).
38. P. Talkner, Ber. Bunsenges. Phys. Chem. 95, 327 (1991).
39. H. Risken, The Fokker-Planck Equation, Springer Series in Synergetics, Vol. 18, Springer, Berlin, New York. (1984).
40. S. Chandrasekhar, Rev. Mod. Phys. 15, 1 (1943).
41. M. C. Wang and G. E. Uhlenbeck, Rev. Mod. Phys. 17, 323 (1945).
42. D. J. Tannor and D. Kohen, J. Chem. Phys. 100, 4932 (1994).
43. A. J. Lichtenberg and M. A. Lieberman, Regular and Stochastic Motion, Applied Mathematic Science Vol. 38, Springer, New York. (1983).
44. D. Kohen, and D. J. Tannor, J. Chem. Phys. 103, 6013 (1995).
45. S. Adelman, J. Chem. Phys. 64, 124 (1976).
46. G. van der Zwan and J. T. Hynes, J. Chem. Phys. 76, 2993 (1982).
47. R. Kubo, M. Toda, N. Hashitsume, in Statistical Physics II, Springer-Verlag, New York, 1991.
48. D. Beece, L. Eisenstein, H. Frauenfelder, D. Good, M. C. Marden, L. Reinisch, A. H. Reynolds, L. B. Sorensen, and K. T. Yue, Biochemistry 19, 5147 (1980).
49. E. H. Rezayi and H. Suhl, Phys. Rev. Lett. 45, 1115 (1980);
50. Phys. Rev B 25, 2323 (1982).
51. C. W. Gardiner, in Handbook of Stochastic Methods, Springer, Berlin, 1983.
52. P. Talkner, Chem. Phys. 180, 199 (1994).
53. A. M. Berezhkovskii, P. Talkner, J. Emmerich and V. Y. Zitserman, J. Chem. Phys. 105, 10890 (1996).
54. E. Pollak and co-workers have also derived a Fokker-Planck-like equation for a non-Markovian friction that at long time limit decays exponentially [E. Pollak, A. M. Berezhkovskii, and Z. Schuss, J. Chem. Phys. 100, 334 (1994)]; our choice of using Adelman's rests only on the fact that this equation will allow us, ultimately, to recover the Hänggi-Mojtabai transmission coefficient.
55. F. Bloch, Phys. Rev. 70, 460 (1946).
56. B. B. Laird, J. Budimir, and J. L. Skinner, J. Chem. Phys. 94, 4391 (1991);
57. J. Budimir and J. L. Skinner, J. Stat. Phys. 49, 1029 (1987).
58. A. G. Redfield, IBM J. Res. Dev. 1, 19 (1957);
59. A. G. Redfield, Adv. Mag. Res. 1, 1 (1965).
60. K. Blum, Density Matrix Theory and Applications, Plenum, New York, 1981.
61. M. Weissbluth, in Phonon-Atom Interactions, Academic Press, New York, 1989.
62. J. M. Jean, R. A. Friesner, and G. R. Fleming, J. Chem. Phys. 96, 5827 (1992).
63. W. T. Pollard and R. A. Friesner, J. Chem. Phys. 100, 5054 (1994).
64. D. W. Oxtoby, Adv. Chem. Phys. 47, 487 (1981).
65. D. Mc Quairie, in Statistical Mechanics, Harper and Row, New York, 1976.
66. L. I. Schiff, in Quantum mechanics, MacGraw-Hill, New York, 1968.
67. J. S. Bader and B. J. Berne, J. Chem. Phys. 100, 8359 (1994).
68. M. Tuckerman and B. J. Berne, J. Chem. Phys. 98, 7301 (1993).
69. E. P. Wigner, Phys. Rev. 40, 747 (1932);
70. M. Hillery, R. F. O'Connell, M. O. Scully, and E. P. Wigner, Phys. Rep. 106, 121 (1984).
71. D. Kohen, C. C. Marston, and D. J. Tannor, J. Chem. Phys. 107, 5236 (1997).
72. F. Haake, in Quantum Statistics and Solid State Physics, Springer Tracts in Modern Physics 60, Springer, Berlin, 1973.
73. H. Haken, Laser Theory, Springer-Verlag, 1970.
74. G. S. Agarwal, Phys. Rev. A 4, 739 (1971).
75. M. Sargent III, M. O. Scully, and W. E. Lamb, Jr., Laser Physics, Addison-Wesley, Reading, Mass. 1974.
76. Ref. [34], p. 425.
77. (a) W. H. Louisell, Quantum Coherence Properties of Radiation, Wiley, New York, 1973, Sect. 6.2;
78. (b) W. H. Louisell and L. R. Walker, Phys. Rev. 137, B204 (1965);
79. (c) M. Lax, Phys. Rev. 145, 100 (1966).
80. C. W. Gardiner, Quantum Noise, Springer-Verlag, New York, 1991, Chapt. 10.
81. R. P. Feynman and F. L. Vernon, Ann. Phys. 24, 118 (1963).
82. A. O. Caldeira and A. J. Leggett, Physica 121A, 587-616 (1983).
83. H. Grabert, P. Schramm, and G.-L. Ingold, Phys. Rep. 168, 115 (1988).
84. P. Talkner, Ann. Phys. 167, 390 (1986), esp. App. B and C.
85. H. Grabert, U. Weiss, and P. Talkner, Z. Phys. B 55, 87 (1984).
86. L. Diosi, Physica A 199, 517-526 (1993);
87. Europhys. Lett. 22, 1-3 (1993).
88. H. Dekker, Phys. Rep. 80, 60 (1981);
89. Phys. Lett. 104 A(2), 67 (1984);
90. H. Dekker, Phys. Rev. A 44, 2314 (1991).
91. G. Lindblad, Commun. Mathem. Phys. 48, 119 (1976).
92. V. Gorini, A. Kossakowski, and E. C. G. Sudarshan, J. Math. Phys. 17, 821 (1976).
93. G. Lindblad, Rep. Math. Phys. 10, 393 (1976).
94. E. B. Davies, Quantum Theory of Open Systems, Academic Press, New York, 1976.
95. R. Alicki and K. Lendi, Quantum Dynamical Semigroups and Applications, Lecture Notes in Physics 286, Springer-Verlag, New York, 1987.
96. W. G. Unruh and W. H. Zurek, Phys. Rev. D 40, 1071-1094 (1989).
97. Y. J. Yan and S. Mukamel, J. Chem. Phys. 89, 5160 (1988).
98. I. Oppenheim and V. Romero-Rochin, Physica 147A, 184 (1987).
99. A. Suarez, R. Silbey, and I. Oppenheim, J. Chem. Phys. 97, 5101 (1992).
100. S. Nakajima, Prog. Theor. Phys. 20, 948 (1958).
101. R. Zwanzig, Lectures in Theoretical Physics, Vol. 3, New York, Interscience, 1961, p. 106.
102. B. J. Berne, in Physical Chemistry: An Advanced Treatise, Vol. 8B, Academic Press, New York, 1971, p. 539.
103. Y. J. Yan and S. Mukamel, J. Chem. Phys. 88, 5735 (1988).
104. P. Pechukas, in Large Scale Molecular Systems, (W. Gans et al., eds.) Plenum, New York, 1991.
105. H. M. Sevian and J. Skinner, J. Chem. Phys. 91, 1775 (1989).
106. N. G. van Kampen, Stochastic Processes in Physics and Chemistry, North-Holland, Amsterdam, The Netherlands, 1992.
107. M. Berman, R. Kosloff, and H. Tal-Ezer, J. Phys. A: Math. Gen. 25, 1283 (1992).
108. P. Pechukas, Phys. Rev. Lett. 73, 1060 (1994).
109. M. A. Sepulveda and F. Grossmann, Adv. Chem. Phys. 96, 191 (1996).
110. Selected Papers on Noise and Stochastic Processes, (N. Wax ed.) Dover, New York, 1954.
111. Ref. [65] pp.
112. A. M. Walsh and R. D. Coalson, Chem. Phys. Lett. 198, 293 (1992).
113. M. J. Ondrechen, A. Nitzan, and M. A. Ratner, Chem. Phys. 16, 49 (1976).
114. K. Lindenberg and B. J. West, Phys. Rev. A 30, 568 (1984).
115. V. Khidekel, Phys. Rev. E 52, 2510 (1995).
116. C. Meier and D. J. Tannor, (J. Chem. Phys. in Press, 1999) in preparation.
117. F. Haake and M. Lewenstein, Phys. Rev. A 28, 3606 (1983).
118. F. Haake and R. Reibold, Phys. Rev. A 32, 2462 (1985).
119. S. Gnutzmann and F. Haake, Z. Phys. B 101, 263 (1996).
120. J. Cao, J. Chem. Phys. 107, 3204 (1997).
121. D. Kohen and D. J. Tannor, J. Chem. Phys. 107, 5141 (1997).
122. D. Kohen, Ph.D. thesis, Univerity of Notre Dame, 1995.
123. G. Ashkenazi, U. Banin, A. Bartana, S. Ruhman, and R. Kosloff, Adv. Chem. Phys. 100, 229 (1997).
124. N. Bohr, H. A. Kramers, and J. C. Slater, Phil. Mag. 47, 785 (1924),
125. reprinted in Sources in Quantum Mechanics, (B. L. van der Waerden, ed.) Dover, 1968.
126. D. Ter Haar, The Old Quantum Theory, Pergamon, 1967, p. 70.
127. A. Pais, Niels Bohr's Times, in Physics, Philosophy, and Polity, Oxford, 1991, pp. 152, 193-194.
128. F. E. Figueiredo and R. M. Levy, J. Chem. Phys. 97, 703 (1992).
129. E. W. Montroll and K. E. Shuler, J. Chem. Phys. 26, 454 (1957).
130. J. I. Steinfeld, J. S. Francisco, and W. L. Hase, in Chemical Kinetics and Dynamics, Prentice-Hall, Englewood Cliffs, N. J., 1989.
131. J. C. Owrutsky, D. Raftery, and R. M. Hochstrasser, Ann. Rev. Phys. Chem. 45, 519 (1994).
132. J. Morelli and D. J. Tannor, Chem. Phys. 235, 213 (1998).
133. J. M. Sancho, A. H. Romero, and K. Lindenberg, J. Chem. Phys., 109, 9888 (1998).
134. J. Ankerhold, H. Grabert, and G. L. Ingold, Phys. Rev. E 51, 4267 (1995).
135. J. Ankerhold and H. Grabert, Phys. Rev. E 52, 4704 (1995).
136. J. Ankerhold and H. Grabert, Phys. Rev. E 55, 1355 (1997).
137. J. Ankerhold and H. Grabert, Chem. Phys. 204, 27 (1996).
138. Y. Tanimura and P. G. Wolynes, Phys. Rev. A 43, 4131 (1991).
139. Y. Tanimura and P. G. Wolynes, J. Chem. Phys. 96, 8485 (1992).
140. N. Makri and D. E. Makarov, Chem. Phys. Lett. 221, 482 (1994).
141. N. Makri and D. E. Makarov, J. Chem. Phys. 102, 4600 (1995).
142. N. Makri and D. E. Makarov, J. Chem. Phys. 102, 4611 (1995).
143. N. Makri, J. Chem. Phys. 109, 2994 (1998).