A new approach to calculating the memory kernel of the generalized quantum master equation for an arbitrary system-bath coupling

Journal of Chemical Physics

Volumn 119, Issue 23, 2003, Pages 12063-12076

  Shi, Qiang ^a   Geva, Eitan ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; CALCULATIONS; COMPUTER SIMULATION; EIGENVALUES AND EIGENFUNCTIONS; ELECTRON TRANSPORT PROPERTIES; HAMILTONIANS; INTEGRAL EQUATIONS; MARKOV PROCESSES; MOLECULAR VIBRATIONS; OPTIMIZATION; PERTURBATION TECHNIQUES; TENSORS;

ARBITRARY SYSTEM BATH COUPLING; GENERALIZED QUANTUM MASTER EQUATION; REDUCED DENSITY OPERATOR;

QUANTUM THEORY;

EID: 0346058207     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1624830     Document Type: Article

References (203)

1. B. J. Berne, G. Ciccotti, and D. F. Coker, Classical and Quantum Dynamics in Condensed Phase Simulations (World Scientific, London, 1998).
2. N. Makri, Annu. Rev. Phys. Chem. 50, 167 (1999).
3. P. Jungwirth and R. B. Gerber, Chem. Rev. 99, 1583 (1999).
4. T. Yamamoto, J. Chem. Phys. 33, 281 (1960).
5. W. H. Miller, J. Chem. Phys. 61, 1823 (1974).
6. W. H. Miller, S. D. Schwartz, and J. W. Tromp, J. Chem. Phys. 79, 4889 (1983).
7. P. Hänggi, P. Talkner, and M. Borkovec, Rev. Mod. Phys. 62, 251 (1990).
8. G. A. Voth, D. Chandler, and W. H. Miller, J. Chem. Phys. 91, 7749 (1989).
9. G. A. Voth, Adv. Chem. Phys. 93, 135 (1996).
10. M. Topaler and N. Makri, J. Chem. Phys. 101, 7500 (1994).
11. N. Makri and K. Thompson, Chem. Phys. Lett. 291, 101 (1998).
12. K. Yamashita and W. H. Miller, J. Chem. Phys. 82, 5475 (1985).
13. E. Rabani, G. Krilov, and B. J. Berne, J. Chem. Phys. 112, 2605 (2000).
14. E. Sim, G. Krilov, and B. Berne, J. Phys. Chem. A 105, 2824 (2001).
15. E. Geva, Q. Shi, and G. A. Voth, J. Chem. Phys. 115, 9209 (2001).
16. Q. Shi and E. Geva, J. Chem. Phys. 116, 3223 (2002).
17. I. Navrotskaya, Q. Shi, and E. Geva, Isr. J. Chem. 42, 225 (2002).
18. D. W. Oxtoby, Adv. Chem. Phys. 47, 487 (1981).
19. D. W. Oxtoby, Annu. Rev. Phys. Chem. 32, 77 (1981).
20. D. W. Oxtoby, J. Phys. Chem. 87, 3028 (1983).
21. J. Chesnoy and G. M. Gale, Ann. Phys. (Paris) 9, 893 (1984).
22. J. Chesnoy and G. M. Gale, Adv. Chem. Phys. 70, 297 (1988).
23. C. B. Harris, D. E. Smith, and D. J. Russell, Chem. Rev. 90, 481 (1990).
24. D. W. Miller and S. A. Adelman, Int. Rev. Phys. Chem. 13, 359 (1994).
25. R. M. Stratt and M. Maroncelli, J. Phys. Chem. 100, 12981 (1996).
26. T. Elsaesser and W. Kaiser, Annu. Rev. Phys. Chem. 42, 83 (1991).
27. J. C. Owrutsky, D. Raftery, and R. M. Hochstrasser, Annu. Rev. Phys. Chem. 45, 519 (1994).
28. S. A. Egorov and J. L. Skinner, J. Chem. Phys. 105, 7047 (1996).
29. S. A. Egorov and J. L. Skinner, J. Chem. Phys. 106, 1034 (1997).
30. S. A. Egorov and B. J. Berne, J. Chem. Phys. 107, 6050 (1997).
31. S. A. Egorov, K. F. Everitt, and J. L. Skinner, J. Phys. Chem. A 103, 9494 (1999).
32. S. A. Egorov and J. L. Skinner, J. Chem. Phys. 112, 275 (2000).
33. K. F. Everitt, S. A. Egorov, and J. L. Skinner, Chem. Phys. 235, 115 (1998).
34. K. F. Everitt and J. L. Skinner, J. Chem. Phys. 110, 4467 (1999).
35. K. F. Everitt, J. L. Skinner, and B. M. Ladanyi, J. Chem. Phys. 116, 179 (2002).
36. E. Rabani and D. R. Reichman, J. Phys. Chem. B 105, 6550 (2001).
37. J. Poulsen, S. R. Keiding, and P. J. Rossky, Chem. Phys. Lett. 336, 448 (2001).
38. J. Poulsen and P. J. Rossky, J. Chem. Phys. 115, 8014 (2001).
39. J. Poulsen and P. J. Rossky, J. Chem. Phys. 115, 8024 (2001).
40. H. Gai and G. A. Voth, J. Chem. Phys. 99, 740 (1993).
41. H. Gai and G. A. Voth, J. Chem. Phys. 101, 1734 (1994).
42. S. Jang, Y. Pak, and G. A. Voth, J. Phys. Chem. A 103, 10289 (1999).
43. Q. Shi and E. Geva, J. Chem. Phys. 118, 7562 (2003).
44. E. T. J. Nibbering, D. A. Wiersma, and K. Duppen, Phys. Rev. Lett. 66, 2464 (1991).
45. E. T. J. Nibbering, D. A. Wiersma, and K. Duppen, Chem. Phys. 183, 167 (1994).
46. M. S. Pshenichnikov, K. Duppen, and D. A. Wiersma, Phys. Rev. Lett. 74, 674 (1995).
47. W. P. de Boeij, M. S. Pshenichnikov, and D. A. Wiersma, Chem. Phys. Lett. 238, 1 (1995).
48. P. Vöhringer et al., J. Chem. Phys. 102, 4027 (1995).
49. T.-S. Yang, P. Vöhringer, D. C. Arnett, and N. F. Scherer, J. Chem. Phys. 103, 8346 (1995).
50. R. Zhang, T.-S. Yang, and A. B. Myers, Chem. Phys. Lett. 211, 541 (1993).
51. T.-S. Yang, R. Zhang, and A. B. Myers, J. Chem. Phys. 100, 8573 (1994).
52. P. Cong, Y. J. Yan, H. P. Deuel, and J. D. Simon, J. Chem. Phys. 100, 7855 (1994).
53. T. Joo, Y. Jia, and G. R. Fleming, J. Chem. Phys. 102, 4063 (1995).
54. T. Joo et al., J. Chem. Phys. 104, 6089 (1996).
55. M. L. Horng, J. A. Gardecki, A. Papazyan, and M. Maroncelli, J. Phys. Chem. 99, 17311 (1995).
56. L. Reynolds et al., J. Phys. Chem. 100, 10337 (1996).
57. S. Mukamel, Principles of Nonlinear Optical Spectroscopy (Oxford, New York, 1995).
58. P. C. Beker et al., Phys. Rev. Lett. 63, 505 (1989).
59. W. P. de Boeij, M. S. Pshenichnikov, and D. A. Wiersma, Annu. Rev. Phys. Chem. 49, 99 (1998).
60. C. J. Bardeen, G. Cerrulo, and C. V. Shank, Chem. Phys. Lett. 280, 127 (1997).
61. M. Cho and G. R. Fleming, J. Chem. Phys. 98, 2848 (1993).
62. J. D. Hybll, A. W. Albrecht, S. M. Gallagher-Faeder, and D. M. Jonas, Chem. Phys. Lett. 297, 307 (1998).
63. D. Zimdars, S. S. Francis, F. C. Ferrante, and M. D. Fayer, J. Chem. Phys. 106, 7498 (1997).
64. R. F. Loring and S. Mukamel, Chem. Phys. Lett. 114, 426 (1985).
65. A. M. Walsh and R. F. Loring, Chem. Phys. Lett. 186, 77 (1991).
66. N. E. Shemetulskis and R. F. Loring, J. Chem. Phys. 97, 1217 (1992).
67. Y. J. Yan and S. Mukamel, J. Chem. Phys. 94, 179 (1991).
68. L. E. Fried, N. Bernstein, and S. Mukamel, Phys. Rev. Lett. 68, 1842 (1992).
69. S. J. Rosenthal et al., J. Mol. Liq. 60, 25 (1994).
70. M. F. Emde, A. Baltuska, A. Kummrow, and M. S. Pshenichnikov, Phys. Rev. Lett. 80, 4645 (1998).
71. M. Cho et al., J. Phys. Chem. 100, 11944 (1996).
72. S. A. Passino, Y. Nagasawa, and G. R. Fleming, J. Chem. Phys. 107, 6094 (1997).
73. S. A. Passino, Y. Nagasawa, T. Joo, and G. R. Fleming, J. Phys. Chem. A 101, 725 (1997).
74. M. J. Lang, X. J. Jordanides, X. Song, and G. R. Fleming, J. Chem. Phys. 110, 5884 (1999).
75. D. S. Larsen, K. Ohta, and G. R. Fleming, J. Chem. Phys. 111, 8970 (1999).
76. K. F. Everitt, E. Geva, and J. L. Skinner, J. Chem. Phys. 114, 1326 (2001).
77. K. F. Everitt and J. L. Skinner, Chem. Phys. 266, 197 (2001).
78. G. R. Fleming and M. Cho, Annu. Rev. Phys. Chem. 47, 109 (1996).
79. S. A. Egorov, M. D. Stephens, and J. L. Skinner, J. Chem. Phys. 107, 10485 (1997).
80. R. Kosloff, J. Phys. Chem. 92, 2087 (1988).
81. C. Leforestier et al., J. Comput. Phys. 94, 59 (1991).
82. R. Kosloff, in Numerical Grid Methods and Their Application to Schrödinger's Equation, edited by C. Cerjan (Kluwer Academic, The Netherlands, 1993), p. 175.
83. R. Kosloff, Annu. Rev. Phys. Chem. 45, 145 (1994).
84. R. Kosloff, in Dynamics of Molecules and Chemical Reactions, edited by D. T. Haar (Dekker, New York, 1996), p. 185.
85. K. Blum, Density Matrix Theory and Applications (Plenum, New York, 1996).
86. S. Nakajima, Prog. Theor. Phys. 20, 948 (1958).
87. R. Zwanzig, Lect. Theor. Phys. 3, 106 (1960).
88. R. Zwanziq, J. Chem. Phys. 33, 1338 (1960).
89. R. Zwanzig, Physica 30, 1109 (1964).
90. I. Prigogine and P. Resibois, Physica 27, 629 (1961).
91. F. Haake, Springer Tracts Mod. Phys. 66, 98 (1973).
92. H. Grabert, Projection Operator Techniques in Nonequilibrium Statistical Mechanics (Springer, Berlin, 1982).
93. R. Alicki and K. Lendi, Quantum Dynamical Semigroups and Applications (Springer, Berlin, 1987).
94. V. May and O. Kühn, Charge and Energy Transfer Dynamics in Molecular Systems (Wiley, Berlin, 2000).
95. R. K. Wangsness and F. Bloch, Phys. Rev. 89, 728 (1953).
96. A. G. Redfield, IBM Syst. J. 1, 19 (1957).
97. B. Yoon, J. M. Deutch, and J. H. Freed, J. Chem. Phys. 62, 4687 (1975).
98. I. Oppenheim, K. E. Shuler, and G. H. Weiss, Stochastic Processes in Chemical Physics: The Master Equation (MIT Press, Cambridge, MA, 1977).
99. S. Mukamel, I. Oppenheim, and J. Ross, Phys. Rev. A 17, 1988 (1978).
100. V. Romero-Rochin and I. Oppenheim, Physica A 155, 52 (1989).
101. V. Romero-Rochin, A. Orsky, and I. Oppenheim, Physica A 156, 244 (1989).
102. N. G. van Kampen, Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 1981).
103. R. Kubo, M. Toda, and N. Hashitsume, Statistical Physics II: Nonequilibrium Statistical Mechanics (Springer, New York, 1985).
104. B. B. Laird, J. Budimir, and J. L. Skinner, J. Chem. Phys. 94, 4391 (1991).
105. W. T. Pollard and R. A. Friesner, J. Chem. Phys. 100, 5054 (1994).
106. W. T. Pollard, A. K. Felts, and R. A. Friesner, Adv. Chem. Phys. XCIII, 77 (1996).
107. E. Geva, R. Kosloff, and J. L. Skinner, J. Chem. Phys. 102, 8541 (1995).
108. E. Geva and R. Kosloff, J. Chem. Phys. 104, 7681 (1996).
109. D. Kohen, C. C. Marston, and D. J. Tannor, J. Chem. Phys. 107, 5236 (1997).
110. J. Cao, J. Chem. Phys. 107, 3204 (1997).
111. Y. J. Yan, Phys. Rev. A 58, 2721 (1998).
112. M. Berman, R. Kosloff, and H. Tal-Ezer, J. Phys. A 25, 1283 (1992).
113. G. Ashkenazi et al., Adv. Chem. Phys. 100, 229 (1997).
114. G. Ashkenazi, R. Kosloff, and M. A. Ratner, J. Am. Chem. Soc. 121, 3386 (1999).
115. R. Kosloff, M. A. Ratner, and W. B. Davis, J. Chem. Phys. 106, 7036 (1997).
116. B. B. Laird and J. L. Skinner, J. Chem. Phys. 94, 4405 (1991).
117. D. R. Reichman and R. J. Silbey, J. Chem. Phys. 104, 1506 (1996).
118. D. R. Reichman, F. L. H. B. Brown, and P. Neu, Phys. Rev. E 55, 2328 (1997).
119. S. Jang, J. Cao, and R. J. Silbey, J. Chem. Phys. 116, 2705 (2002).
120. A. Suárez and R. Silbey, J. Chem. Phys. 94, 4809 (1991).
121. D. Li and G. A. Voth, J. Phys. Chem. 95, 10425 (1991).
122. R. Silbey and R. A. Harris, J. Phys. Chem. 93, 7062 (1989).
123. M. Sparpaglione and S. Mukamel, J. Chem. Phys. 88, 3263 (1988).
124. A. A. Golosov and D. R. Reichman, J. Chem. Phys. 115, 9848 (2001).
125. A. A. Golosov and D. R. Reichman, J. Chem. Phys. 115, 9862 (2001).
126. R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965).
127. L. S. Schulman, Techniques and Applications of Path Integration (Wiley, New York, 1981).
128. H. Kleinert, Path Integrals in Quantum Mechanics, Statistics and Polymer Physics (World Scientific, NJ, 1995).
129. R. P. Feynman and F. L. Vernon Jr., Ann. Phys. (N.Y.) 24, 118 (1963).
130. P. G. Wolynes, Phys. Rev. Lett. 47, 968 (1981).
131. A. O. Caldeira and A. J. Leggett, Ann. Phys. (N.Y.) 149, 374 (1983).
132. R. D. Coalson, J. Chem. Phys. 86, 995 (1987).
133. C. Mak and D. Chandler, Phys. Rev. A 44, 2352 (1991).
134. M. Topaler and N. Makri, J. Chem. Phys. 97, 9001 (1992).
135. M. Topaler and N. Makri, Chem. Phys. Lett. 210, 285 (1993).
136. M. Topaler and N. Makri, Chem. Phys. Lett. 210, 448 (1993).
137. M. Topaler and N. Makri, J. Phys. Chem. 100, 4430 (1996).
138. D. E. Makarov and N. Makri, Chem. Phys. Lett. 221, 482 (1994).
139. N. Makri and D. Makarov, J. Chem. Phys. 102, 4600 (1995).
140. N. Makri and D. Makarov, J. Chem. Phys. 102, 4611 (1995).
141. N. Makri, J. Math. Phys. 36, 2430 (1995).
142. N. Makri, E. Sim, D. E. Makarov, and M. Topaler, Proc. Natl. Acad. Sci. U.S.A. 93, 3926 (1996).
143. E. Sim and N. Makri, Comput. Phys. Commun. 99, 335 (1997).
144. E. Sim and N. Makri, J. Phys. Chem. B 101, 5446 (1997).
145. N. Makri, J. Phys. Chem. A 102, 4414 (1998).
146. J. S. Shao and N. Makri, J. Chem. Phys. 116, 507 (2002).
147. A. A. Golosov, R. A. Friesner, and P. Pechukas, J. Chem. Phys. 110, 138 (1999).
148. A. A. Golosov, R. A. Friesner, and P. Pechukas, J. Chem. Phys. 112, 2095 (2000).
149. K. Thompson and N. Makri, J. Chem. Phys. 13, 1343 (1999).
150. K. Thompson and N. Makri, Phys. Rev. E 59, R4729 (1999).
151. G. D. Billing, Chem. Phys. Lett. 30, 391 (1975).
152. G. D. Billing, J. Chem. Phys. 99, 5849 (1993).
153. J. C. Tully and R. K. Preston, J. Chem. Phys. 55, 562 (1971).
154. J. C. Tully, J. Chem. Phys. 93, 1061 (1990).
155. P. J. Kuntz, J. Chem. Phys. 95, 141 (1991).
156. A. I. Krylov et al., J. Chem. Phys. 104, 3651 (1996).
157. E. Gallicchio and B. J. Berne, J. Chem. Phys. 105, 7064 (1996).
158. E. Gallicchio, S. A. Egorov, and B. J. Berne, J. Chem. Phys. 109, 7745 (1998).
159. S. A. Egorov, E. Gallicchio, and B. J. Berne, J. Chem. Phys. 107, 9312 (1997).
160. G. Krilov and B. J. Berne, J. Chem. Phys. 111, 9147 (1999).
161. E. Rabani, D. R. Reichman, G. Krylov, and B. J. Berne, Proc. Natl. Acad. Sci. U.S.A. 99, 1129 (2002).
162. A. A. Golosov, D. R. Reichman, and E. Rabani, J. Chem. Phys. 118, 457 (2003).
163. J. Cao and G. A. Voth, J. Chem. Phys. 100, 5106 (1994).
164. J. Cao and G. A. Voth, J. Chem. Phys. 101, 6157 (1994).
165. J. Cao and G. A. Voth, J. Chem. Phys. 101, 6168 (1994).
166. S. Jang and G. A. Voth, J. Chem. Phys. 111, 2357 (1999).
167. S. Jang and G. A. Voth, J. Chem. Phys. 111, 2371 (1999).
168. D. R. Reichman, P.-N. Roy, S. Jang, and G. A. Voth, J. Chem. Phys. 113, 919 (2000).
169. A. Calhoun, M. Pavese, and G. A. Voth, Chem. Phys. Lett. 262, 415 (1996).
170. U. W. Schmitt and G. A. Voth, J. Chem. Phys. 111, 9361 (1999).
171. M. Pavese and G. A. Voth, Chem. Phys. Lett. 249, 231 (1996).
172. K. Kinugawa, P. B. Moore, and M. L. Klein, J. Chem. Phys. 106, 1154 (1997).
173. K. Kinugawa, P. B. Moore, and M. L. Klein, J. Chem. Phys. 109, 610 (1998).
174. K. Kinugawa, Chem. Phys. Lett. 292, 454 (1998).
175. M. Pavese, D. R. Bernard, and G. A. Voth, Chem. Phys. Lett. 300, 93 (1999).
176. D. R. Reichman and E. Rabani, Phys. Rev. Lett. 87, 265702 (2001).
177. E. Rabani and D. R. Reichman, J. Chem. Phys. 116, 6271 (2002).
178. E. Rabani and D. R. Reichman, Phys. Rev. E 65, 036111 (2002).
179. D. R. Reichman and E. Rabani, J. Chem. Phys. 116, 6279 (2002).
180. H. Wang, X. Sun, and W. H. Miller, J. Chem. Phys. 108, 9726 (1998).
181. E. Pollak and J. Liao, J. Chem. Phys. 108, 2733 (1998).
182. W. H. Miller, Adv. Chem. Phys. 25, 69 (1974).
183. W. H. Miller, J. Chem. Phys. 53, 3578 (1970).
184. M. F. Herman and E. Kluk, Chem. Phys. 91, 27 (1984).
185. E. J. Heller, J. Chem. Phys. 94, 2723 (1981).
186. K. G. Kay, J. Chem. Phys. 100, 4377 (1994).
187. M. Ovchinnikov and V. A. Apkarian, J. Chem. Phys. 105, 10312 (1996).
188. M. Ovchinnikov and V. A. Apkarian, J. Chem. Phys. 108, 2277 (1998).
189. X. Sun and W. H. Miller, J. Chem. Phys. 106, 916 (1997).
190. W. H. Miller, Faraday Discuss. 110, 1 (1998).
191. J. S. Shao and N. Makri, J. Phys. Chem. A 103, 7753 (1999).
192. K. Thompson and N. Makri, Phys. Rev. E 59, R4729 (1999).
193. O. Kühn and N. Makri, J. Phys. Chem. A 103, 9487 (1999).
194. H. Wang, M. Thoss, and W. H. Miller, J. Chem. Phys. 112, 47 (2000).
195. M. Ovchinnikov, V. A. Apkarian, and G. A. Voth, J. Chem. Phys. 184, 7130 (2001).
196. W. H. Miller, J. Phys. Chem. A 105, 2942 (2001).
197. N. Makri and W. H. Miller, J. Chem. Phys. 116, 9207 (2002).
198. A. Bartana, R. Kosloff, and D. J. Tannor, J. Chem. Phys. 106, 1435 (1997).
199. E. Geva, J. Chem. Phys. 116, 1629 (2001).
200. M. Demirplak and S. A. Rice, J. Chem. Phys. 116, 8028 (2002).
201. Y. Ohtsuki, K. Nakagami, W. Zhu, and H. Rabitz, Chem. Phys. 287, 197 (2003).
202. S. A. Rice, and M. Zhao, Optical Control of Molecular Dynamics (Wiley, New York, 2000).
203. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes (Cambridge University Press, Cambridge, MA, 1986).