Research on models of open quantum system interacted with bath

Jie YANG; Shuang CONG

doi:10.3969/j.issn.1007-5461.2011.06.004

[3] Esposito M, Gaspard P. Quantum master equation for a system influencing its environment ［J］. Phys. Rev. E, 2003, 68: 066112.

[4] Zwolak M P. Dynamics and Simulation of Open Quantum Systems ［D］. Pasadena California: California Institute of Technology, 2008.

[5] Xu R, Cui P, Li X, et al. Exact quantum master equation via the calculus on path integrals ［J］. The Journal of Chemical Physics, 2005, 122: 041103.

[6] Stefanescu E, Scheid W, Sandulescu A. Non-Markovian master equation for a system of Fermions interacting with an electromagnetic field ［J］. Annals of Physics, 2008, 323(5): 1168-1190.

[7] Weiss U. Quantum Dissipative Systems ［M］. 3rd ed., Singapore: World Scientific, 2008: 101-105.

[8] Gambetta J M. Non-Markovian Stochastic Schrodinger Equations and Interpretations of Quantum Mechanics ［D］. Queensland: Doctoral Dissertation of Griffith University, 2003.

[9] Sommerfeld G A, et al. Probleme der modernen physik ［M］. Festschrift zum 60, Hirzel, Leipzig, 1928: 30.

[10] Redfield A G. On the theory of relaxation processes ［J］. IBM J. Res. Dev., 1957, 1: 19-31.

[11] Thomas W, Richard P, Friesner A. Solution of the Redfield equation for the dissipation quantum dynamics of multilevel systems ［J］. J. Chem. Phys., 1994, 100: 5054.

[12] Wu J. Non-equilibrium stationary states from the equation of motion of open systems ［J］. New Journal of Physics, 2010, 12: 083042.

[13] Lindblad G. On the generators of quantum dynamical semigroups ［J］. Commun. Math. Phys., 1976, 48: 119-130.

[14] Gaspard P, Nagaoka M. Slippage of initial conditions for the Redfield master equation ［J］. J. Chem. Phys., 1999, 111: 5668-5675.

[15] Suarez A, Silbey R, Oppenheim I. Memory effects in the relaxation of quantum open systems ［J］. J. Chem. Phys., 1992, 97: 5101.

[16] Strunz W T. The Brownian motion stochastic Schrodinger equation ［J］. Chem. Phys., 2001, 268: 237-248.

[17] Esposito M, Gaspard P. Quantum master equation for a system influencing its environment ［J］. Phys. Rev. E, 2003, 68(6): 066112.

[18] Kraus K. States, Effects and Operations: Fundamental Notions of Quantum Theory ［M］. Berlin: Springer-Verlag, 1983: 151-167.

[19] Melikidze A. Quantum Mechanics of Open Systems ［D］. Princeton: Princeton University, 2001.

[20] Brauer H P. Exact quantum jump approach to open systems in bosonic and spin baths ［J］. Phys. Rev. A, 2004, 69: 022115.

[21] Gutmann H P G. Description and Control of Decoherence in Quantum Bit Systems ［D］. Munchen: Ludwig-Maximilians University, 2005.

[22] Gorini V, Kossakowski A, Sudarshan E C G. Completely positive dynamical semigroups of N-level systems ［J］. J. Math. Phys., 1976, 17: 821-825.

[23] Dacies E B. Markovian master equations ii. ［J］. Mathematical Annals, 1976, 219: 147-158.

[24] Schirmer S G, Solomon A G. Construction on relaxation rates for N-level quantum systems ［J］. Phys. Rev. A, 2004, 70: 022107.

[25] Daffer S L. Markovian and Non-Markovian State Evolution in Open Quantum Systems ［D］. Albuquerque, New Mexico: University of New Mexico, 1999.

[26] Sifel C, Hohenester U. Optically triggered spin entanglement of electrons in semiconductors ［J］. Semiconductor Science and Technology, 2004, 19: S403.

[27] Luczka J. On Markovian kinetic equations: Zubarev’s nonequilibrium statistical operator approach ［J］. Physica A, 1989, 149: 245-266.

[28] Celio M, Loss D. Comparison between different Markov approximations for open spin systems ［J］. Physica A, 1989, 158: 769-783.

[29] Scully M O, Zubairy M S. Quantum Optics ［M］. Cambridge, England: Cambridge University Press, 1997: 255-256.

[30] Michael R G. Models for local Ohmic quantum dissipation ［J］. Phys. Rev. A, 1993, 48(2): 1028-1034.

[31] Caldeira A O, Leggett A J. Influence of damping on quantum interference: An exactly soluble model ［J］. Phys. Rev. A, 1985, 31: 1059.

[32] Dodonov A V, Mizrahi S S, Dodonov V V. Quantum master equations from classical Lagrangians with two stochastic forces ［J］. Phys. Rev. E, 2007, 75: 011132.

[33] Havas P. The range of application of the Lagrange formalism I ［J］. Nuovo. Cimento. Suppl., 1957, 5: 363.

[34] Oreshkov O. Topics in Quantum Information and the Theory of Open Quantum Systems ［D］. Los Angeles: University of Southern California, 2008.

[35] Krovi K, Oreshkov O, Ryazanov M, et al. Non-Markovian dynamics of a qubit coupled to an ising spin bath ［J］. Phys. Rev. A, 2007, 76: 052117.

[36] Shabani A, Lidar D A. Completely positive post-Markovian master equation via a measurement approach ［J］. Phys. Rev. A, 2005, 71(2): 020101.

[37] Cohen D, Kottos T. Quantum dissipation due to the interaction with chaotic degrees of freedom and the correspondence principle ［J］. Phys. Rev. Lett., 1999, 82: 4951-4955.

[38] Marcus R A. Ion pairing and electron transfer ［J］. Adv. Chem. Phys., 1997, 101: 391-408.

[39] Deng Y, et al. Vibrational energy relaxation of polyatomic molecules in liquids: the solvent’s perspective ［J］. J. Chem. Phys., 2002, 117: 1735-1749.