Non-Markovian dynamics of open quantum systems: Stochastic equations and their perturbative solutions

Annals of Physics

Volumn 327, Issue 4, 2012, Pages 1238-1276

  Fleming, C H ^a   Hu, B L ^a  

^a Bldg 142   (United States)

Author keywords

Langevin equation; Master equation; Non Markovian dynamics; Nonequilibrium quantum statistical mechanics; Nonequilibrium thermodynamics; Open quantum system

Indexed keywords

EID: 84856537009     PISSN: 00034916     EISSN: 1096035X     Source Type: Journal    
DOI: 10.1016/j.aop.2011.12.006     Document Type: Article

References (57)

1. Kampen N., Oppenheim I. J. Stat. Phys. 1997, 87:1325.
2. Breuer H.P., Ma A., Petruccione F. Quantum Computing and Quantum Bits in Mesoscopic Systems 2003, Kluwer, Dordrecht. arxiv:quant-ph/0209153, A.J. Leggett, B. Ruggiero, P. Silvestrini (Eds.).
3. Strunz W.T., Yu T. Phys. Rev. A 2004, 69:052115.
4. Pollard W.T., Felts A.K., Friesner R.A. Adv. Chem. Phys. 1997, 93:77.
5. Carmichael H.J. Statistical Methods in Quantum Optics I 1999, Springer, New York.
6. Breuer H.P., Petruccione F. The Theory of Open Quantum Systems 2002, Oxford University Press, New York.
7. Kampen N.G.V. Adv. Chem. Phys. 2007, 34:245.
8. Lindblad G. Comm. Math. Phys. 1976, 48:119.
9. Gorini V., Kossakowski A., Sudarshan E.C.G. J. Math. Phys. 1976, 17:821.
10. C.H. Fleming, B.L. Hu, A. Roura, Decoherence strength of multiple non-Markovian environments, 2010. [quant-ph]. arxiv:1011.3286.
11. C.H. Fleming, B.L. Hu, A. Roura, Non-equilibrium fluctuation-dissipation inequality, and non-equilibrium uncertainty principle, 2010. [quant-ph]. arxiv:1012.0681.
12. Fleming C.H., Cummings N.I., Anastopoulos C., Hu B.L. J. Phys. A 2010, 43:405304.
13. Fleming C.H., Cummings N.I. Phys. Rev. E 2011, 83:031117.
14. Fleming C.H., Roura A., Hu B.L. Phys. Rev. E 2011, 84:021106.
15. C.H. Fleming, N.I. Cummings, C. Anastopoulos, B.L. Hu, Non-Markovian entanglement of two-level atoms in an electromagnetic field, J. Phys. A (2012) (in press). [quant-ph]. arxiv:1012.5067.
16. Y. Subasi, C.H. Fleming, J.M. Taylor, B.L. Hu, The equilibrium states of small systems (2011) (in preparation).
17. Swain S. J. Phys. A 1981, 14:2577.
18. Fleming C.H., Roura A., Hu B.L. Ann. Phys. 2011, 326:1207.
19. Scala M., Militello B., Messina A., Maniscalco S., Piilo J., Suominen K. J. Phys. A 2007, 40:14527.
20. Hu B.L., Paz J.P., Zhang Y. Phys. Rev. D 1992, 45:2843.
21. Xu R.X., Mo Y., Cui P., Lin S.H., Yan Y.J. Prog. Theoret. Chem. Phys. 2003, 12:7.
22. De Vega I., Alonso D. Phys. Rev. A 2006, 73:022102.
23. Scala M., Militello B., Messina A., Piilo J., Maniscalco S. Phys. Rev. A 2007, 75:013811.
24. Scala M., Militello B., Messina A., Maniscalco S., Piilo J., Suominen K.A. J. Phys. A 2007, 40:14527.
25. Pechukas P. Phys. Rev. Lett. 1994, 73:1060.
26. Shaji A., Sudarshan E. Phys. Lett. A 2005, 341:48.
27. C. Ling, J. Nie, L. Qi, Y. Ye, Bi-quadratic optimization over unit spheres and semidefinite programming relaxations, 2008.
28. Choi M.-D. Linear Algebra Appl. 1975, 10:285.
29. Kraus K. States, Effects and Operations: Fundamental Notions of Quantum Theory 1983, Springer-Verlag, Berlin.
30. Kossakowski A. Rep. Math. Phys. 1972, 3:247.
31. Davies E.B. Comm. Math. Phys. 1974, 39:91.
32. Davies E.B. Math. Ann. 1976, 219:147.
33. Davies E.B. Rep. Math. Phys. 1977, 11:169.
34. Alicki R., Lendi K. Quantum Dynamical Semigroups and Applications 2007, Springer.
35. Accardi L., Lu Y.G., Volovich I.V. Quantum Theory and its Stochastic Limit 2002, Springer.
36. Attal S., Joye A., Pillet C.-A. Open Quantum Systems II: The Markovian Approach 2006, Springer.
37. Ingarden R.S., Kossakowski A., Ohya M. Information Dynamics and Open Systems: Classical and Quantum Approach 1997, Kluwer Academic, Dordrecht.
38. Lindblad G. Non-Equilibrium Entropy and Irreversibility 1983, D. Reidel, Dordrecht.
39. Weiss U. Quantum Dissipative Systems 1993, World Scientific, Singapore.
40. Petz D., Sudár C. J. Math. Phys. 1996, 37:2662.
41. Rivas A., Huelga S.F. Open Quantum Systems: An Introduction 2011, Springer.
42. C.H. Fleming, Non-Markovian dynamics of open quantum systems, Ph.D. Thesis, University of Maryland College Park, 2011.
43. Feynman R.P., Vernon F.L. Ann. Phys. 1963, 24:118.
44. Magnus W. Comm. Pure Appl. Math 1954, 7:649.
45. Blanes S., Casas F., Oteo J.A., Ros J. J. Phys. A 1998, 31:259.
46. C.H. Fleming, P.R. Johnson, B.L. Hu, Nonequilibrium dynamics of charged-particles in an electromagnetic field: causal and stable dynamics from 1/c expansion of QED, 2011. [quant-ph]. arxiv:1106.1886.
47. Fer F. Bull. Cl. Sci. Acad. R. Belg. 1958, 44:818.
48. Paz J.P., Zurek W.H. Phys. Rev. Lett. 1999, 82:5181.
49. Briegel H.J., Englert B.G. Phys. Rev. A 1993, 47:3311.
50. C.H. Fleming, Canonical-like perturbation theory with time dependence (2011) (in preparation).
51. Nakajima S. Progr. Theoret. Phys. 1958, 20:948.
52. Zwanzig R. J. Chem. Phys. 1960, 33:1338.
53. Ford G.W., Lewis J.T., O'Connell R.F. Phys. Rev. A 1988, 37:4419.
54. Caldeira A.O., Leggett A.J. Phys. Rev. Lett. 1981, 46:211.
55. Bhatia R. Positive Definite Matrices 2007, Princeton University Press, Princeton, Oxford.
56. Kubo R. J. Phys. Soc. Japan 1957, 12:570.
57. Martin P.C., Schwinger J. Phys. Rev. 1959, 115:1342.