Superoperator representation of nonlinear response: Unifying quantum field and mode coupling theories

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

Volumn 68, Issue 2 1, 2003, Pages

  Mukamel, Shaul ^a  

^a UNIVERSITY OF ROCHESTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; FERMIONS; GREEN'S FUNCTION; HYDRODYNAMICS; MATHEMATICAL OPERATORS; PERTURBATION TECHNIQUES; VECTORS;

HILBERT SPACE OPERATORS; KELDYSH LOOPS; LIOUVILLE SPACE; MATSUBARA CONTOURS; SUPEROPERATOR;

QUANTUM THEORY;

EID: 42749108860     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (94)

1. J.W. Negele and H. Orland, Quantum Many-Particle Systems (Peresus, Cambridge, MA, 1988).
2. A.L. Fetter and J.D. Walecka, Quantum Theory of Many-Particle Systems (McGraw-Hill, New York, 1971).
3. S. Doniach and E.H. Sondheimer, Green Functions for Solid State Physicists (Benjamin, Reading, MA, 1974).
4. A.A. Abrikosov, L.P. Gorkov, and I.Ye. Dzyaloshinsky, Quantum Field Theoretical Methods in Statistical Physics (Oxford University Press, Oxford, 1965).
5. L.P. Kadanoff and G. Baym, Quantum Statistical Mechanics (Benjamin, Menlo Park, CA, 1962).
6. G.D. Mahan, Many-Particle Physics (Plenum, New York, 1990).
7. H. Haug and A.P. Jauho, Quantum Kinetics in Transport and Optics of Semiconductors (Springer, Berlin, 1996).
8. P. Ring and P. Schuck, The Nuclear Many-Body Problem (Springer-Verlag, New York, 1980)
9. J.-P. Blaizot and G. Ripka, Quantum Theory of Finite Systems (MIT Press, Cambridge, MA, 1986).
10. D.J. Thouless, The Quantum Mechanics of Many-Body Systems (Academic, New York, 1972).
11. J. Schofield, R. Lim, and I. Oppenheim, Physica A 181, 89 (1992).
12. D. Ronis, Physica A 99, 403 (1979)
13. D. Ronis, Physica A 107, 25 (1981).
14. D.R. Reichman and E. Rabani, Phys. Rev. Lett. 87, 265702 (2001)
15. R.A. Denny and D.R. Reichman, J. Chem. Phys. 116, 1979 (2002)
16. R.A. Denny and D.R. Reichman, J. Chem. Phys. 116, 1987 (2002).
17. R. van Zon and J. Schofield, Phys. Rev. E 65, 011106 (2002)
18. R. van Zon and J. Schofield, Phys. Rev. E 65, 011107 (2002).
19. J. Machta and I. Oppenheim, Physica A 122, 361 (1982).
20. R.A. Denny, D.R. Reichman, and J.-P. Bouchaud, Phys. Rev. Lett. 90, 025503 (2003).
21. K. Kawasaki, Ann. Phys. (N.Y.) 61, 1 (1970).
22. J.-P. Bouchaud, L. Cugliandolo, J. Kurchan, and M. Mézard, Physica A 226, 243 (1996).
23. W. Götze, in Liquids, Freezing and Glass Transition, Proceedings of the Les Houch Summer School of Theoretical Physics, 1989, edited by J.P. Hansen, D. Levesque, and J. Zimm-Justin (North-Holland, Amsterdam, 1989)
24. W. Götze and L. Sjögren, Rep. Prog. Phys. 55, 241 (1992).
25. E.N. Economou, Green's Function in Quantum Physics (Springer-Verlag, Berlin, 1983).
26. L.V. Keldysh, Zh. Éksp Teor. Fiz. 47, 1515 (1964) [Sov. Phys. JETP 20, 1018 (1965)]
27. J. Schwinger, J. Math. Phys. 2, 407 (1961)
28. E.M. Lifshitz and L.P. Pitaevsky, Physical Kinetics (Pergamon, Oxford, 1981).
29. T. Matsubara, Prog. Theor. Phys. 14, 351 (1955).
30. R. Kubo, M. Toda, and N. Hashitsume, Statistical Physics II, 2nd ed. (Springer, Berlin, 1991).
31. S. Mukamel, Principles of Nonlinear Optical Spectroscopy (Oxford University Press, New York, 1995).
32. V. Chernyak, N. Wang, and S. Mukamel, Phys. Rep. 263, 213 (1995).
33. V. Chernyak and S. Mukamel, J. Chem. Phys. 108, 5812 (1998).
34. S. Mukamel, A. Piryatinski, and V. Chernyak, J. Chem. Phys. 110, 1711 (1999).
35. E.J. Heller, J. Chem. Phys. 65, 4979 (1976)
36. F. Grossmann and E.J. Heller, Chem. Phys. Lett. 241, 45 (1995).
37. M. A. Sepúlveda and S. Mukamel, J. Chem. Phys. 102, 9327 (1995).
38. M. Ovchinnikov, V.A. Apkarian, and G.A. Voth, J. Chem. Phys. 114, 7130 (2001)
39. M. Ovchinnikov and V.A. Apkarian, ibid. 108, 2277 (1998).
40. K. Thompson and N. Makri, Phys. Rev. E 59, 4729 (1999)
41. K. Thompson and N. Makri, Chem. Phys. Lett. 291, 101 (1998).
42. W.H. Miller, Faraday Discuss. 110, 1 (1998)
43. X. Sun and W.H. Miller, J. Chem. Phys. 110, 6635 (1999)
44. H. Wang, M. Thoss, and W.H. Miller, ibid. 112, 47 (2000).
45. T. Keyes, P. Moore, and G. Seeley, in Proceedings of XXIII Winter Meeting on Statistical Physics; Cuernavaca, Mexico, 1994 (World Scientific, Singapore, 1994).
46. J. Kim and T. Keyes, Phys. Rev. E 65, 061102 (2002).
47. S. Saito and I. Ohmine, J. Chem. Phys. 108, 240 (1998)
48. S. Saito and I. Ohmine, Phys. Rev. Lett. 88, 207401 (2002).
49. J. Cao, S. Yang, and J. Wu, J. Chem. Phys. 116, 3760 (2002)
50. J. Cao, J. Wu, and S. Yang, ibid. 116, 3739 (2002).
51. R.A. Denny and D.R. Reichman, Phys. Rev. E 63, 065101(R) (2001).
52. T.I.C. Jansen, J.G. Snijders, and K. Duppen, J. Chem. Phys. 113, 307 (2000)
53. T.I.C. Jansen, J.G. Snijders, and K. Duppen, J. Chem. Phys. 114, 10 910 (2001).
54. Y. Tanimura and S. Mukamel, J. Chem. Phys. 99, 9496 (1993)
55. V. Khidekel and S. Mukamel, Chem. Phys. Lett. 240, 304 (1995).
56. A. Ma and R.M. Stratt, Phys. Rev. Lett. 85, 1004 (2000).
57. K. Okumura and Y. Tanimura, Chem. Phys. Lett. 278, 175 (1997)
58. M. Cho, K. Okumura, and Y. Tanimura, J. Chem. Phys. 108, 1326 (1998).
59. V. Chernyak and S. Mukamel, J. Chem. Phys. 105, 4565 (1996).
60. U. Fano, Rev. Mod. Phys. 29, 74 (1957)
61. U. Fano, Phys. Rev. 131, 259 (1963)
62. U. Fano in Lectures on Many-Body Problems, edited by E.R. Caianiello (Academic, New York, 1964), p. 217.
63. A. Ben Reuven, Adv. Chem. Phys. 33, 235 (1975).
64. R. Zwanzig, Lect. Theor. Phys. 3, 106 (1961)
65. R. Zwanzig, Physica (Amsterdam) 30, 1109 (1964)
66. R. Zwanzig, J. Chem. Phys. 33, 1338 (1960)
67. R. Zwanzig, Nonequilibrium Statistical Mechanics (Oxford University Press, New York, 2001).
68. V. Khidekel, V. Chernyak, and S. Mukamel, in Femtochemistry, edited by M. Chergui (World Scientific, Singapore, 1996), p. 507.
69. J. Schwinger, J. Math. Phys. 2, 407 (1961).
70. P.C. Martin, Measurements and Correlation Functions (Gordon and Breach, New York, 1968).
71. R.J. Glauber, in Quantum Optics and Electronics, edited by C. DeWitt, A. Blandin, and C. Cohen-Tannoudji (Gordon and Breach, New York, 1965).
72. M. Brach and R.K. Bhadur, Semiclassical Physics (Addison-Wesley, New York, 1997).
73. V. Chernyak and S. Mukamel, J. Chem. Phys. 100, 2953 (1994).
74. Y.J. Yan and S. Mukamel, J. Chem. Phys. 89, 5160 (1988).
75. M. Gell-Mann and F.E. Low, Phys. Rev. 84, 350 (1951).
76. C. Jarzynski, Phys. Rev. Lett. 78, 2690 (1997)
77. C. Jarzynski, Phys. Rev. E 56, 5018 (1997).
78. D. Frenkel and B. Smit, Understanding Molecular Simulation: From Algorithms to Applications (Academic, London, 2002).
79. S. Mukamel, Phys. Rev. Lett. 90, 170604 (2003).
80. F. Wilczek and A. Shapere, Geometric Phases in Physics (World Scientific, Singapore, 1989).
81. A.O. Caldeira and A.J. Leggett, Physica A 121, 587 (1983).
82. A.G. Redfield, Adv. Magn. Reson. 1, 1 (1965).
83. V. Khidekel, V. Chernyak, and S. Mukamel, J. Chem. Phys. 105, 8543 (1996).
84. L.E. Fried and S. Mukamel, Adv. Chem. Phys. 84, 435 (1993).
85. P. Egelsteff, Adv. Phys. 11, 203 (1962)
86. J. Borysow, M. Moraldi, and L. Frommhold, Mol. Phys. 56, 913 (1985).
87. W.P. Schleich, Quantum Optics in Phase Space (Wiley, New York, 2001).
88. S. Mukamel, V. Khidekel, and V. Chernyak, Phys. Rev. E 53, 1 (1996).
89. C. Dellago and S. Mukamel, Phys. Rev. E 67, 035205 (2003).
90. A. Donoso and C.C. Martens, J. Chem. Phys. 116, 10 598 (2002)
91. A. Donoso and C.C. Martens, Phys. Rev. Lett. 87, 223202 (2001)
92. A. Donoso and C.C. Martens, J. Chem. Phys. 102, 4291 (1998).
93. R.P. Feynman, Statistical Mechanics (Benjamin, Reading, MA, 1972).
94. L.S. Schulman, Techniques and Applications of Path Integration (Wiley, New York, 1981).