跳至主要内容

Time Dependent Entropy and Decoherence in a Modified Quantum Damped Harmonic Oscillator

Read full paper at:
http://www.scirp.org/journal/PaperInformation.aspx?PaperID=52402#.VJOW_cCAM4

The time dependence of probability and Shannon entropy of a modified damped harmonic oscillator is studied by using single and double Gaussian wave functions through the Feynman path method. We establish that the damped coefficient as well as the system frequency and the distance separating two consecutive waves of the initial double Gaussian function influences the coherence of the system and can be used to control its decoherence.
Cite this paper
Pelap, F. , Fomethe, A. , Fotue, A. and Tabue, M. (2014) Time Dependent Entropy and Decoherence in a Modified Quantum Damped Harmonic Oscillator. Journal of Quantum Information Science, 4, 214-226. doi: 10.4236/jqis.2014.44020
 

[1] Isar, A. (2005) Decoherence in Open Quantum Systems. Romanian Journal of Physics, 50, 147-156.
[2] Walls, D.F. and Millburn, G.J. (1994) Quantum Optics. Springer, Heildelberg.
[3] Scully, M.O. and Zubairy, M.S. (1997) Quantum Optics. Cambridge University Press, Cambridge.
http://dx.doi.org/10.1017/CBO9780511813993
[4] Sargent III, M., Scully, M.O. and Lamb Jr., W.E. (1974) Laser Physics. Addison-Wesley, Reading.
[5] Nielsen, M.A. and Chuang, I.L. (2000) Quantum Computation and Quantum Information. Cambridge University, Cambridge, UK.
[6] Karlsson, E.B. (1998) Coherence and Decoherence of Positive Particle States in Solids. Physica Scripta, 76, 179.
http://dx.doi.org/10.1238/Physica.Topical.076a00179
[7] Chatzidimitriou-Dreismann, C.A., Abdul-Redah, T. and Kolaric, B. (2001) Entanglement of Protons in Organic Molecules: An Attosecond Neutron Scattering Study of C [Bond] H Bond Breaking. Journal of the American Chemical Society, 123, 11945-11951.
http://dx.doi.org/10.1021/ja004186d
[8] Chatzidimitriou-Dreismann, C.A., Abdul Redah, T., Streffer, R.M. and Mayers, J. (1997) Anomalous Deep Inelastic Neutron Scattering from Liquid H2O-D2O: Evidence of Nuclear Quantum Entanglement. Physical Review Letters, 79, 2839-2842.
http://dx.doi.org/10.1103/PhysRevLett.79.2839
[9] Krzywicki, A. (1993) Coherence and Decoherence in Radiation off Colliding Heavy Ions. Physical Review D, 48, 5190-5195.
http://dx.doi.org/10.1103/PhysRevD.48.5190
[10] Zeh, H.D. (1986) Emergence of a Classical Universe from Quantum Gravity and Cosmology. Physics Letters A, 116, 9-12.
http://dx.doi.org/10.1016/0375-9601(86)90346-4
[11] Zeh, H.D. (1988) Time in Quantum Gravity. Physics Letters A, 126, 311-317.
http://dx.doi.org/10.1016/0375-9601(88)90842-0
[12] Zeh, H.D. (1992) The Physical Basis of the Direction of Time. Springer, Berlin.
http://dx.doi.org/10.1007/978-3-662-02759-2
[13] Kiefer, C. (1987) Emergence of a Classical Universe from Quantum Gravity and Cosmology. Classical and Quantum Gravity, 4, 1369-1382.
http://dx.doi.org/10.1088/0264-9381/4/5/031
[14] Halliwell, J. (1989) Decoherence in Quantum Cosmology. Physical Review D, 39, 2912-2923.
http://dx.doi.org/10.1103/PhysRevD.39.2912
[15] Barvinsky, A.O. and Kamenshchik, A.Y. (1990) Preferred Basis in the Many-Worlds Interpretation of Quantum Mechanics and Quantum Cosmology. Classical and Quantum Gravity, 7, 2285-2293.
http://dx.doi.org/10.1088/0264-9381/7/12/010
[16] Barvinsky, A.O. and Kamenshchik, A.Y. (1995) Preferred Basis in Quantum Theory and the Problem of Classicalizationof the Quantum Universe. Physical Review D, 52, 743-757.
http://dx.doi.org/10.1103/PhysRevD.52.743
[17] Brandenberger, R., Laflamme, R. and Mijic, M. (1990) Modern Physics Letters A, 5, 2311.
[18] Paz, J.-P. and Sinha, S. (1991) Decoherence and Back Reaction: The Origin of the Semiclassical Einstein Equations. Physical Review D, 44, 1038-1049.
http://dx.doi.org/10.1103/PhysRevD.44.1038
[19] Paz, J.-P. and Sinha, S. (1992) Decoherence and Back Reaction in Quantum Cosmology: Multidimensional Minisuperspace Examples. Physical Review D, 45, 2823-2842.
http://dx.doi.org/10.1103/PhysRevD.45.2823
[20] Castagnino, M.A., Gangui, A., Mazzitelli, F.D. and Tkachev, I.I. (1993) Third Quantization, Decoherence and the Interpretation of Quantum Gravity in Mini-Super-Space. Classical and Quantum Gravity, 10, 2495-2504.
http://dx.doi.org/10.1088/0264-9381/10/12/008
[21] Kefer, C. and Zeh, H.D. (1995) Arrow of Time in a Recollapsing Quantum Universe. Physical Review D, 51, 4145-4153.
http://dx.doi.org/10.1103/PhysRevD.51.4145
[22] Mensky, M.B. and Novikov, I.D. (1996) Decoherence Caused by Topology in a Time-Machine Spacetime. International Journal of Modern Physics D, 5, 1-27.
http://dx.doi.org/10.1142/S0218271896000023
[23] Giulini, D., Joos, E., Kiefer, C., Kupsch, J., Stamatescu, I.O. and Zeh, H.D. (1996) Decoherence and the Appearance of a Classical World in Quantum Theory. Springer, Berlin.
http://dx.doi.org/10.1007/978-3-662-03263-3
[24] Paz, J.P. and Zurek, W.H. (2001) In Coherent Atomic Matter Waves. In: Kaiser, R., Westbrook, C. and David F., Eds., Les Houches Session LXXII, Springer, Berlin, 533-614.
[25] Zurek, W.H. (2003) Decoherence, Einselection, and the Quantum Origins of the Classical. Reviews of Modern Physics, 75, 715-775.
http://dx.doi.org/10.1103/RevModPhys.75.715
[26] Morikawa, M. (1990) Quantum Decoherence and Classical Correlation in Quantum Mechanics. Physical Review D, 42, 2929-2932.
http://dx.doi.org/10.1103/PhysRevD.42.2929
[27] Habib, S. and Laflamme, R. (1990) Wigner Function and Decoherence in Quantum Cosmology. Physical Review D, 42, 4056-4065.
http://dx.doi.org/10.1103/PhysRevD.42.4056
[28] Alicki, R. (2004) Pure Decoherence in Quantum Systems. Open Systems & Information Dynamics (OSID), 11, 53-61.
http://dx.doi.org/10.1023/B:OPSY.0000024755.58888.ac
[29] Joos, E., Zeh, H.D., Kiefer, C., Giulini, D., Kupsch, J. and Stamatescu, I.O. (2003) Decoherence and the Appearance of a Classical World in Quantum Theory. Springer, Berlin.
http://dx.doi.org/10.1007/978-3-662-05328-7
[30] Gamble, J.K. and Lindner, J.F. (2009) Demystifying Decoherence and the Master Equation of Quantum Brownian Motion. American Journal of Physics, 77, 244.
http://dx.doi.org/10.1119/1.3043847
[31] Zuo, J. and O’Connell, R.F. (2004) Effect of an External Field on Decoherence: Part II. Journal of Modern Optics, 51, 821-832.
http://dx.doi.org/10.1080/09500340408233599
[32] Ozcan, O., Akturk, E. and Sever, R. (2008) Time Dependence of Joint Entropy of Oscillating Quantum Systems. International Journal of Theoretical Physics, 47, 3207-3218.
http://dx.doi.org/10.1007/s10773-008-9756-4
[33] Isar, A. (2007) Quantum Decoherence of a Damped Harmonic Oscillator. Optics and Spectroscopy, 103, 252-257.
http://dx.doi.org/10.1134/S0030400X07080140
[34] Lindblad, G. (1976) Brownian Motion of a Quantum Harmonic Oscillator. Reports on Mathematical Physics, 10, 393-406.
http://dx.doi.org/10.1016/0034-4877(76)90029-X
[35] Sandulescu, A. and Scutaru, H. (1987) Open Quantum Systems and the Damping of Collective Models in Deep Inelastic Collisions. Annals of Physics, 173, 277-317.
http://dx.doi.org/10.1016/0003-4916(87)90162-X
[36] Elran, Y. and Brumer, P. (2004) Decoherence in an Inharmonic Oscillator Coupled to a Thermal Environment: A Semi-Classical Forward-Backward Approach. The Journal of Chemical Physics, 121, 2673.
http://dx.doi.org/10.1063/1.1766009
[37] Chruscinski, D. and Jurkowski, J. (2010) Memory in a Nonlocally Damped Oscillator. In: Accardi, L., Freudenberg, W. and Ohya, M., Eds., Quantum Bio-Informatics III, Tokyo University of Science, Tokyo, 155-166.
http://dx.doi.org/10.1142/9789814304061_0014
[38] Bateman, H. (1931) On Dissipative Systems and Related Variational Principles. Physical Review, 38, 815-819.
http://dx.doi.org/10.1103/PhysRev.38.815
[39] Caldirola, P. (1941) Quantum Analysis of Modified Caldirola-Kanai Oscillator Model for Electromagnetic Fieldsin Time-Varying. IL Nuovo Cimento, 18, 393-400.
http://dx.doi.org/10.1007/BF02960144
[40] Feynman, R.P. (1948) Space-Time Approach to Non-Relativistic Quantum Mechanics. Reviews of Modern Physics, 20, 367-387.
http://dx.doi.org/10.1103/RevModPhys.20.367
[41] Fai, L.C., Fomethe, A., Mborong, V.B., Fotue, A.J., Domngang, S., Issofa, N. and Tchoffo, M. (2008) Polaron State Screening by Plasmons in a Spherical Nanocrystal. Journal of Low Temperature Physics, 152, 71-87.
http://dx.doi.org/10.1007/s10909-008-9803-9
[42] Um, C.I., Yeon, K.H. and George, T.F. (2002) The Quantum Damped Harmonic Oscillator. Physics Reports, 362, 63-192.
http://dx.doi.org/10.1016/S0370-1573(01)00077-1
[43] Um, C.I., Yeon, K.H. and Kahng, W.H. (1987) The Quantum Damped Driven Harmonic Oscillator. Journal of Physics A: Mathematical and General, 20, 611-626.
http://dx.doi.org/10.1088/0305-4470/20/3/024
[44] Feynman, R.P. and Hibbs, A.R. (1965) Quantum Mechanics and Path Integrals. McGraw-Hill, New York.                            eww141219lx

评论

此博客中的热门博文

Does Immigration Promote the Investment of the Monopolistic Firm?

In the present paper, we examine the effect of increasing uncertainty of immigrants’ growth on the optimal timing of investment of a firm that has a monopolistic power over the labor market. It is revealed that when the uncertainty of immigrants’ growth is more than a threshold level, increasing uncertainty of immigrants’ growth accelerates the optimal timing of firms’ investment and enhances the economic growth, even if the uncertainty of immigrants’ growth is formulated by the geometric Brownian motion, which is in sharp contrast to the standard result that an increase in the uncertainty postpones the optimal timing. With an increase in the immigrants over the past ten years, workforces in the host countries have been growing significantly to the extent that the immigrants represent 70% of the increase in the workforce in Europe, and 47% in the United States as OECD indicates. In the present paper, we attempted to investigate the effect of increased uncertainty caused by the growi...

Education Policy Implementation: A Mechanism for Enhancing Primary Education Development in Zanzibar

Education is one of the fundamental rights of individuals; therefore, the government of a country needs to develop and strengthen educational policy and quality as well as to ensure that everyone has equal access to basic education. The improvement of access and quality of education in the world is becoming as an essential factor in development, whereas the basic education (primary school), is acknowledged as a foundation of the higher educational development for every country. To fulfill this goal, governments introduce several policies and procedures; however, it requires some reforms and participation from the politician, policymakers, and other stakeholders to re-examine educational policy so that it can lead to multiplication and betterment of the reforms. Educational reforms actually focus on accountability. A positive educational development and reform is very challenging and needs more effort and strategy on how to use and utilize the resources effectively as such it can achie...