Abstract
Non-Markovian reduced dynamics of an open system is investigated. In the case when the initial state of the reservoir is the vacuum state, an approximation is introduced which makes it possible to construct a reduced dynamics which is completely positive.
Similar content being viewed by others
References
R. Alicki, K. Lendi, Quantum Dynamical Semigroups and Applications, Lecture Notes in Phys. Vol. 286, Springer-Verlag, 1987.
Breuer H.-P. and Petruccione F. (2002). The theory of open quantum systems. Oxford University Press, New York
Nielsen M.A. and Chuang I.L. (2000). Quantum computation and quantum information. Cambridge University Press, Cambridge
Feynman R.P. and Vernon F.L. (1963). Ann. Physics 24: 118
Weiss U. (1999). Quantum Dissipative Systems. World Scientific, Singapore
Legget A.J., Chakravarty S., Dorsey A.T., Fisher M.P.A., Garg. A. and Zwegler W. (1987). Rev. Mod. Phys. 59: 1
Nakajima S (1958). Prog. Theor. Phys 20: 948
Zwanzig R. (1960). J. Chem. Phys 33: 1338
Gorini V., Kossakowski A. and Sudarshan E.C.G. (1976). J. Math. Phys. 17: 821
Lindblad G. (1976). Commun. Math. Phys. 48: 119
K. Kraus, States, Effects and Operations, Fundamental notions of Quantum Theory, Academics, Berlin, 1983.
Shibata N. and Takahashi Y. (1977). J. Stat. Phys. 17: 171
Imamoglu A. (1994). Phys. Rev. A 50: 3650
Royer A. (1996). Phys. Rev. Lett. 77: 3272
Royer A. (2003). Phys. Lett. A 315: 335
Barnett M. and Stenholm S. (2001). Phys. Rev. A 64: 033808
Breuer H.-P., Kappler B. and Petruccione F. (2001). Ann. Physics 291(1): 36–70
Breuer H.-P. and Petruccione F. (2001). Phys. Rev. A 63: 032102
Breuer H.-P., Kappler B. and Petruccione F. (1999). Phys. Rev. A 59: 1633
Breuer H.-P. (2004). Phys. Rev. A 69: 022115
Breuer H.-P. (2004). Phys. Rev. A 70: 012106
Breuer H.-P., Gemmer J. and Michel M. (2006). Phys. Rev. E 73(1): 016139
Maniscalco S. (2005). Phys. Rev. A 72: 024103
Maniscalco S. and Petruccione F. (2006). Phys. Rev. A 73: 012111
Wilkie J. (2000). Phys. Rev. E 62: 8808
Wilkie J. (2001). J. Phys. A 114: 7736
Breuer H.-P. (2007). Phys. Rev. A 75: 022103
Budini A. (2004). Phys. Rev. A 69: 042107
A. Budini, quant-ph/0601140.
Budini A. (2006). Phys. Rev. A 74: 053815
Shabani A. and Lidar D. (2005). Phys. Rev. A 71: 020101
Lee J., Kim I., Ahn D., Mc Aneney H. and Kim M.S. (2004). Phys. Rev. A 70: 024301
Gamov G. (1928). Z. Phys. 51: 204
A. Bohm, M. Gadella, Dirac kets, Gamov vectors and Gel’fand triples, Lecture Notes in Physics Vol. 348, Springer-Verlag, 1989.
Gelfand I. and Vilenkin N. (1964). Generalized Functions, Vol. 4. Academic Press, New York
K. Maurin, General Eigenfunction Expansions and Unitary Representations of Topological Groups, PWN, Warszawa, 1968.
Prigogine I. (1980). From Being to Becoming. Freeman, New York
Prigogine I. (1992). Phys. Rep. 219: 93
Petrovski T. and Prigogine I. (1991). Physica A 174: 146
Petrovski T., Prigogine I. and Tasaki S. (1991). Physica A 173: 175
Antoniou I. and Tasaki S. (1992). Physica A 190: 303
Antoniou I. and Tasaki S. (1993). Int. J. Quant. Chem. 44: 425
Antoniou I. and Prigogine I. (1993). Physica A 192: 443
Antoniou I., Gadella M. and Pronko G. (1998). J. Math. Phys. 39: 2459
Antoniou I., Gadella M., Pronko M.P.I. and Pronko G. (1998). J. Math. Phys. 39: 2995
Civitarese O. and Gadella M. (2004). Phys. Rep. 396: 41
Friedrichs K. (1948). Commun. Pure Appl. Math. 1: 361
Ruuskanen P. (1970). Nucl. Phys. B 22: 253
Stey G. and Gibberd R. (1972). Physica A 60: 1
Davies E. (1974). J. Math. Phys. 15: 2036
Bayley T. and Schieve W. (1978). Nuovo Cimento A 47: 231
Antoniou I., Karpov E.P.G. and Yarevski E. (2003). Int. J. Theor. Phys. 42: 2403
Facci P. and Pascazio S. (1998). Phys. Lett. A 241: 139
Facci P. and Pascazio S. (1999). Physica A 271: 138
Garraway B. and Dalton B. (2006). J. Phys. B 39: S767
C. Anastopoulos, S. Shresta, B. Lu, quant-ph/0610007.
Yoo H. (1985). J. Eberly, Phys. Rep. 118: 239
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kossakowski, A., Rebolledo, R. On non-Markovian Time Evolution in Open Quantum Systems. Open Syst Inf Dyn 14, 265–274 (2007). https://doi.org/10.1007/s11080-007-9051-5
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11080-007-9051-5