Abstract
The low frequency profile of the initial distribution of coherent states of a bosonic environment may control and hinder the dissipation of energy and model the dynamics of a strongly coupled quantum oscillator. The energy of the main oscillator is asymptotically stabilized to its initial value with damped oscillations enveloped in inverse power law decays in addition to pure inverse power law relaxations. Two limiting regimes appear. Arbitrarily slowly damped oscillations around the initial value show oscillating exchange of energy with the environment. For special initial conditions the inverse power law relaxations prevail over long times on the oscillations and the dissipation of energy may be hindered by slowing down arbitrarily the decays.
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References
U. Weiss, Quantum Dissipative Systems, 3rd edn. (World Scientific, Singapore, 2008)
E.B. Davies, Quantum Theory of Open Systems (Academic Press, London, 1976)
H.-P. Breuer, F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, Oxford, 2002)
G.S. Agarwal, Phys. Rev. A 4, 739 (1971)
F. Haake, in Springer Tracts in Modern Physics (Springer, Heidelberg, 1973), Vol. 66
A.O. Caldeira, A.J. Leggett, Phys. Rev. Lett. 46, 211 (1981)
A.J. Leggett, S. Chakravarty, A.T. Dorsey, M.P.A. Fisher, A. Garg, W. Zwerger, Rev. Mod. Phys. 59, 1 (1987)
A.O. Caldeira, A.J. Leggett, Physica A 121, 587 (1983)
C. Morais Smith, A.O. Caldeira, Phys. Rev. A 36, 3509 (1987)
A.O. Caldeira, A.J. Leggett, Ann. Phys. 149, 374 (1983)
Dynamics of Dissipation, edited by P. Garbaczewski, R. Olkiewicz, Lecture Notes in Physics (Springer, Berlin, 2003), Vol. 597
W.H. Louisell, Quantum Statistical Properties of Radiation (Wiley, New York, 1973)
H. Carmichael, An Open Systems Approach to Quantum Optics, Lectures Notes in Physics (Springer-Verlag, Berlin, 1993)
W.H. Zurek, Rev. Mod. Phys. 75, 715 (2003)
D. Giulini, E. Joos, C. Kiefer, J. Kupsch, I.O. Stomatescu, H.D. Zeh, Decoherence and the Appearance of Classical World in Quantum Theory (Springer, Berlin, 1996)
G.W. Ford, M. Kac, P. Mazur, J. Math. Phys. 6, 504 (1965)
F. Haake, R. Reibold, Phys. Rev. A 32, 2462 (1985)
G.W. Ford, M. Kac, J. Stat. Phys. 6, 803 (1987)
H. Grabert, P. Schramm, G.-L. Ingold, Phys. Rep. 168, 115 (1988)
B.L. Hu, J.P. Paz, Y. Zhang, Phys. Rev. D 45, 2843 (1992)
J.P. Paz, W.H. Zurek, in Coherent Atomic Matter Waves, Proceedings of the 72nd Les Hounches Summer School, edited by R. Kaiser, C. Westbrook, F. David (Springer-Verlag, Berlin, 1999)
G.W. Ford, R.F. O’Connell, Phys. Rev. D 64, 105020 (2001)
W. Aschbacher, V. Jaksić, Y. Pautrat, C.-A. Pillet, in Open Quantum Systems III: Recent Developements, in volume 1882 of Lecture Notes in Mathematics, edited by S. Attal, A. Joyce, C.-A. Pillet (Springer, Berlin, 2006)
R.P. Feynman, F.L. Vernon, Ann. Phys. 24, 118 (1963)
J.P. Paz, S. Habib, W.H. Zurek, Phys. Rev. D 47, 488 (1993)
W.H. Zurek, S. Habib, J.P. Paz, Phys. Rev. Lett. 70, 1187 (1993)
L.D. Romero, J.P. Paz, Phys. Rev. A 55, 4070 (1997)
J.R. Anglin, J.P. Paz, W.H. Zurek, Phys. Rev. A 55, 4041 (1997)
G.W. Ford, R.F. O’Connel, Phys. Rev. D 64, 105020 (2001)
D.F. Walls, G.J. Milbourn, Phys. Rev. A 31, 2403 (1985)
C.M. Savage, D.F. Walls, Phys. Rev. A 32, 2316 (1985)
S.M. Dutra, Eur. J. Phys. 18, 194 (1997)
S.M. Dutra, J. Mod. Opt. 45, 759 (1998)
F. Intravia, S. Maniscalco, A. Messina, Phys. Rev. A 67, 042108 (2003)
W.H. Zurek, Rev. Mod. Phys. 75, 715 (2003)
I. Joichi, Sh. Matsumoto, M. Yoshimura, Phys. Rev. A 57, 798 (1998)
P. Hänggi, P. Talkner, M. Borkovec, Rev. Mod. Phys. 62, 251 (1990)
M. Rosenau da Costa, A.O. Caldeira, S.M. Dutra, H. Westfahl, Phys. Rev. A 61, 022107 (2000)
C. Fleming, N.I. Cummings, C. Anastopoulos, B.L. Hu, J. Phys. A 43, 405304 (2010)
S. Garmon, T. Petrosky, L. Simine, D. Segal, Fortschr. Phys. 61, 261 (2013)
B. Praux, R. Bhatt, P.L. Knight, Phys. Rev. A 41, 6296 (1990)
C.W. Gardiner, P. Zoller, Quantum Noise, 3rd edn. (Springer, Berlin, Heidelberg, New York, 2004)
F. Walls, G.J. Milburn, Quantum Optics, 2nd edn. (Springer, 2008)
C. Cohen-Tannoudji, J. Dupont-Roc, G. Grynberg, Atom-Photon Interactions/Basics Processes and Applications (John Wiley & Sons, New York, 1992)
X. Xiao, Y.-B. Gao, Commun. Theor. Phys. 58, 251 (2012)
A. Pereverzev, Phys. Rev. E 68, 026111 (2003)
F. Giraldi, F. Petruccione, Open Syst. Inform. Dyn. 20, 1350002 (2013)
F. Giraldi, F. Petruccione, J. Phys. A 46, 015304 (2013)
C.W. Gardiner, P. Zoller, Quantum Noise, 3rd edn. (Springer Berlin Heidelberg, New York, 2004)
E.C. Titchmarsh, The Theory of functions, 2nd edn. (Oxford University Press, 1997)
E.C. Titchmarsh, Introduction to the Theory of Fourier Integrals, 2nd edn. (Chelsea Pub. Co., New York, 1986)
A. Erdélyi, W. Magnus, F. Oberhettinger, F. Tricomi, Tables of Integral Transforms (McGraw-Hill, New York, 1954), Vol. 2
R. Wong, Yu-Qiu Zhao, Proc. R. Soc. Lond. A 458, 625 (2002)
R. Wong, Asymptotic Approximations of Integrals (Academic Press, Boston, 1989)
H.S. Wall, Analytic Theory of Continued Fractions (D. Van Nostrand Company Inc., 1948)
E.B. Davies, Commun. Math. Phys. 33, 171 (1973)
E. Braun, Physica A 129, 262 (1985)
P.S. Riseborough, P. Hänggi, U. Weiss, Phys. Rev. A 31, 471 (1985)
S.F. Norelykke, H. Flyvbjerg, Phys. Rev. E 83, 041103 (2011)
R. Martinazzo, M. Nest, P. Saalfrank, G.F. Tantardini, J. Chem. Phys. 125, 194102 (2006)
H.M. Wiseman, J. Vaccaro, Phys. Rev. A 65, 043606 (2002)
I. Burghardt, R. Martinazzo, K.H. Hughes, J. Chem. Phys. 137, 144107 (2012)
R.J. Glauber, Phys. Rev. 131, 2766 (1963)
E.C.G. Sudarshan, Phys. Rev. Lett. 10, 277 (1963)
N.-H. Tong, M. Vojta, Phys. Rev. Lett. 97, 016802 (2006)
D. Porras, F. Marquardt, J. von Delft, J.I. Cirac, Phys. Rev. 782, 010101(R) (2008)
J.T. Barreiro, M. Müller, P. Schindler, D. Nigg, T. Monz, M. Chwalla, M. Hennrich, C.F. Roos, P. Zoller, R. Blatt, Nature 470, 486 (2011)
K.W. Murch, U. Vool, D. Zhou, S.J. Weber, S.M. Girvin, I. Siddiqi, Phys. Rev. Lett. 109, 183602 (2012)
F. Giraldi, F. Petruccione, Eur. Phys. J. D 67, 178 (2013) and references therein
A.D. Polyanin, A.V. Manzhirov, Handbook of Integral Equations (Chapman & Hall/CRC Press, 2008)
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Giraldi, F., Petruccione, F. Control of dissipation of energy via reservoirs of coherent states. Eur. Phys. J. D 68, 24 (2014). https://doi.org/10.1140/epjd/e2013-40602-7
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DOI: https://doi.org/10.1140/epjd/e2013-40602-7