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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access July 17, 2012

Non-Markovianity and initial correlations for the generalized Lindblad master equation

Huang Xiao-Li, Shao-Cheng Hou, Lin-Cheng Wang and Xue-Xi Yi
From the journal Open Physics

Abstract

Taking a two-level system interacting with a two-band environment as an example, we discuss the non-Markovianity and initial system-environment correlations for the generalized Lindblad master equation by using a recently introduced measure given by Breuer et al. Our results show that the initial states of the environment and initial system-environment correlations have strong effects on the non-Markovianity of the reduced system. Moreover, we also show that information and energy can flow in different directions, i.e., energy flows to the system while information flows from the system, which is quite different from previous results.

[1] H.P. Breuer, F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, Oxford, 2001) Search in Google Scholar

[2] G. Lindblad, Commun. Math. Phys. 48, 119 (1976) http://dx.doi.org/10.1007/BF0160849910.1007/BF01608499Search in Google Scholar

[3] J.Q. Liao, H. Dong, X.G. Wang, X.F. Liu, C.P. Sun, arXiv:0909.1230 Search in Google Scholar

[4] H.P. Breuer, E.M. Laine, J. Piilo, Phys. Rev. Lett. 103, 210401 (2009) http://dx.doi.org/10.1103/PhysRevLett.103.21040110.1103/PhysRevLett.103.210401Search in Google Scholar PubMed

[5] E.M. Laine, J. Piilo, H.P. Breuer, Phys. Rev. A 81, 062115 (2010) http://dx.doi.org/10.1103/PhysRevA.81.06211510.1103/PhysRevA.81.062115Search in Google Scholar

[6] M.M. Wolf, J. Eisert, T.S. Cubitt, J. I. Cirac, Phys. Rev. Lett. 101, 150402 (2008) http://dx.doi.org/10.1103/PhysRevLett.101.15040210.1103/PhysRevLett.101.150402Search in Google Scholar PubMed

[7] A.K. Rajagopal, A.R. Usha Devi, R. W. Rendell, Phys. Rev. A 82, 042107 (2010) 10.1103/PhysRevA.82.042107Search in Google Scholar

[8] X.M. Lu, W.G. Wang, C.P. Sun, Phys. Rev. A 82, 042103 (2010) http://dx.doi.org/10.1103/PhysRevA.82.04210310.1103/PhysRevA.82.042103Search in Google Scholar

[9] A. Rivas, S.F. Huelga, M. B. Plenio, Phys. Rev. Lett. 105, 050403 (2010) http://dx.doi.org/10.1103/PhysRevLett.105.05040310.1103/PhysRevLett.105.050403Search in Google Scholar PubMed

[10] S.C. Hou, X.X. Yi, S.X. Yu, C.H. Oh, Phys. Rev. A 83, 062115 (2011) http://dx.doi.org/10.1103/PhysRevA.83.06211510.1103/PhysRevA.83.062115Search in Google Scholar

[11] L. Mazzola, E.M. Laine, H.P. Breuer, S. Maniscalco, J. Piilo, Phys. Rev. A 81, 062120 (2010) http://dx.doi.org/10.1103/PhysRevA.81.06212010.1103/PhysRevA.81.062120Search in Google Scholar

[12] J.G. Li, J. Zou, B. Shao, Phys. Rev. A 81, 062124 (2010) http://dx.doi.org/10.1103/PhysRevA.81.06212410.1103/PhysRevA.81.062124Search in Google Scholar

[13] E. Andersson, J.D. Cresser, M.H. W. Hall, arXiv:1009.0845 Search in Google Scholar

[14] Z.Y. Xu, W.L. Yang, M. Feng, Phys. Rev. A 81, 044105 (2010) arXiv:0912.2879 http://dx.doi.org/10.1103/PhysRevA.81.04410510.1103/PhysRevA.81.044105Search in Google Scholar

[15] P. Haikka, J.D. Cresser, S. Maniscalco, Phys. Rev. A 83, 012112 (2011) arXiv:1011.5328 http://dx.doi.org/10.1103/PhysRevA.83.01211210.1103/PhysRevA.83.012112Search in Google Scholar

[16] D. Chruscinski, A. Kossakowski, Á. Rivas, Phys. Rev. A 83, 052128 (2011) http://dx.doi.org/10.1103/PhysRevA.83.05212810.1103/PhysRevA.83.052128Search in Google Scholar

[17] A. Shabani, D.A. Lidar, Phys. Rev. A 71, 020101 (2005) http://dx.doi.org/10.1103/PhysRevA.71.02010110.1103/PhysRevA.71.020101Search in Google Scholar

[18] E.M. Laine, J. Piilo, H.P. Breuer, Europhys. Lett. 92, 60010 (2010) http://dx.doi.org/10.1209/0295-5075/92/6001010.1209/0295-5075/92/60010Search in Google Scholar

[19] A. Smirne, H.P. Breuer, J. Piilo, B. Vacchini, Phys. Rev. A 82, 062114 (2010) http://dx.doi.org/10.1103/PhysRevA.82.06211410.1103/PhysRevA.82.062114Search in Google Scholar

[20] H.P. Breuer, Phys. Rev. A 75, 022103 (2007) http://dx.doi.org/10.1103/PhysRevA.75.02210310.1103/PhysRevA.75.022103Search in Google Scholar

[21] H.P. Breuer, J. GemPhys. Rev. E 73, 016139 (2006) http://dx.doi.org/10.1103/PhysRevE.73.01613910.1103/PhysRevE.73.016139Search in Google Scholar PubMed

[22] J. Gemmer, M. Michel, Europhys. Lett. 73, 1 (2006) http://dx.doi.org/10.1209/epl/i2005-10363-010.1209/epl/i2005-10363-0Search in Google Scholar

[23] J. Gemmer, M. Michel, G. Mahher, Quantum Thermodynamics, Lect. Notes Phys. 784, 216 (Springer-Verlag, Berlin, 2009) Search in Google Scholar

[24] J. Gemmer, M. Michel, Physica E 29, 136 (2005) http://dx.doi.org/10.1016/j.physe.2005.05.01110.1016/j.physe.2005.05.011Search in Google Scholar

[25] X.L. Huang, X. X. Yi, Europhys. Lett. 82, 50001 (2008) http://dx.doi.org/10.1209/0295-5075/82/5000110.1209/0295-5075/82/50001Search in Google Scholar

[26] X.L. Huang, X. X. Yi, C. F. Wu, X. L. Feng, S. X. Yu, C. H. Oh, Phys. Rev. A 78, 062114 (2008) http://dx.doi.org/10.1103/PhysRevA.78.06211410.1103/PhysRevA.78.062114Search in Google Scholar

Published Online: 2012-7-17
Published in Print: 2012-8-1

© 2012 Versita Warsaw

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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