Initial-Slip Term Effects on the Dissipation-Induced Transition of a Simple Harmonic Oscillator

Funds: Supported by the National Natural Science Foundation of China under Grant No 11275100, and the K. C. Wong Magna Foundation of Ningbo University.
  • Received Date: November 08, 2016
  • Published Date: December 31, 2016
  • We investigate the effects of the initial-slip term by studying the dissipation-induced transition probabilities between any two eigenstates of a simple harmonic oscillator. The general analytical expressions for the transition probabilities are obtained, then the special cases of transition probabilities ignoring the Brownian motion from the ground state to the first few excited states are discussed. It is found that the initial-slip term not only makes the forbidden transitions between states of different parity possible but also lifts the initial value of the transition probabilities.
  • Article Text

  • [1]
    Weiss U 1999 Quantum Dissipative Systems Singapore: World Scientific

    Google Scholar

    [2]
    Caldeira A O and Leggett A J 1981 Phys. Rev. Lett. 46 211 doi: 10.1103/PhysRevLett.46.211

    CrossRef Google Scholar

    [3]
    Caldeira A O and Leggett A J 1983Ann. Phys. 149 374 doi: 10.1016/0003-49168390202-6

    CrossRef Google Scholar

    [4]
    Ford G W and Kac M 1987 J. Stat. Phys. 46 803 doi: 10.1007/BF01011142

    CrossRef Google Scholar

    [5]
    Ford G W et al. 1988 Phys. Rev. A 37 4419 doi: 10.1103/PhysRevA.37.4419

    CrossRef Google Scholar

    [6]
    Leggett A J et al. 1987 Rev. Mod. Phys. 59 1 doi: 10.1103/RevModPhys.59.1

    CrossRef Google Scholar

    [7]
    You B and Cen L X 2015 Acta Phys. Sin. 64 210302 in Chinese

    Google Scholar

    [8]
    Breuer H P and Petruccione F 2002 The Theory of Open Quantum Systems Oxford: Oxford University Press

    Google Scholar

    [9]
    Carmichael H 1993 An Open System Approach to Quantum Optics Berlin: Springer

    Google Scholar

    [10]
    Feng X Q et al. 2016 Acta Phys. Sin. 65 044205 in Chinese

    Google Scholar

    [11]
    Zwanzig 1973 J. Stat. Phys. 9 215 doi: 10.1007/BF01008729

    CrossRef Google Scholar

    [12]
    Ingold G L 2002 Lect. Notes Phys. 611 1 doi: 10.1007/3-540-45855-7_1

    CrossRef Google Scholar

    [13]
    Bez W 1980 Z. Phys. B 39 319 doi: 10.1007/BF01305831

    CrossRef Google Scholar

    [14]
    Cortés E et al. 1985 J. Chem. Phys. 82 2708 doi: 10.1063/1.448268

    CrossRef Google Scholar

    [15]
    Canizares J S and Sols F 1994 Physica A 212 181 doi: 10.1016/0378-43719490146-5

    CrossRef Google Scholar

    [16]
    Feynman R P 1948 Rev. Mod. Phys. 20 367 doi: 10.1103/RevModPhys.20.367

    CrossRef Google Scholar

    [17]
    Feynman R P and Hibbs A R 1965 Quantum Mechanics and Path Integrals New York: McGraw-Hill

    Google Scholar

    [18]
    Dekker H 1981 Phys. Rep. 80 1 and references therein doi: 10.1016/0370-15738190033-8

    CrossRef Google Scholar

    [19]
    Um C I et al. 2002 Phys. Rep. 362 63 and references therein doi: 10.1016/S0370-15730100077-1

    CrossRef Google Scholar

    [20]
    Feynman R and Vernon F L 1963 Ann. Phys. N. Y. 24 118 doi: 10.1016/0003-49166390068-X

    CrossRef Google Scholar

    [21]
    Caldeira A O and Leggett A J 1983 Physica A 121 587 doi: 10.1016/0378-43718390013-4

    CrossRef Google Scholar

    [22]
    Hakim V and Ambegaokar V 1985 Phys. Rev. A 32 423 doi: 10.1103/PhysRevA.32.423

    CrossRef Google Scholar

    [23]
    Haake F and Reibold R 1985 Phys. Rev. A 32 2462 doi: 10.1103/PhysRevA.32.2462

    CrossRef Google Scholar

    [24]
    Unruh W G and Zurek W H 1989 Phys. Rev. D 40 1071 doi: 10.1103/PhysRevD.40.1071

    CrossRef Google Scholar

    [25]
    Grabert H et al. 1988 Phys. Rep. 168 115 doi: 10.1016/0370-15738890023-3

    CrossRef Google Scholar

    [26]
    Halliwell J J and Zoupas A 1995 Phys. Rev. D 52 7294 doi: 10.1103/PhysRevD.52.7294

    CrossRef Google Scholar

    [27]
    Hu B L et al. 1992 Phys. Rev. D 45 2843 doi: 10.1103/PhysRevD.45.2843

    CrossRef Google Scholar

    [28]
    Hu B L et al. 1993 Phys. Rev. D 47 1576 doi: 10.1103/PhysRevD.47.1576

    CrossRef Google Scholar

    [29]
    Halliwell J J and Yu T 1996 Phys. Rev. D 53 2012 doi: 10.1103/PhysRevD.53.2012

    CrossRef Google Scholar

    [30]
    Chou C H et al. 2008 Phys. Rev. E 77 011112 doi: 10.1103/PhysRevE.77.011112

    CrossRef Google Scholar

    [31]
    Yu L Y and Sun C P 1994 Phys. Rev. A 49 592 doi: 10.1103/PhysRevA.49.592

    CrossRef Google Scholar

    [32]
    Yu L Y 1995 Phys. Lett. A 202 167 doi: 10.1016/0375-96019500274-7

    CrossRef Google Scholar

    [33]
    Landovitz L F et al. 1979 Phys. Rev. A 20 1162 doi: 10.1103/PhysRevA.20.1162

    CrossRef Google Scholar

    [34]
    Landovitz L F et al. 1980 J. Math. Phys. 21 2159 doi: 10.1063/1.524724

    CrossRef Google Scholar

    [35]
    Landovitz L F et al. 1983 J. Chem. Phys. 78 291 doi: 10.1063/1.444499

    CrossRef Google Scholar

    [36]
    Um C I et al. 1987J. Phys. A 20 611 doi: 10.1088/0305-4470/20/3/024

    CrossRef Google Scholar

    [37]
    Croxson P 1994 Phys. Rev. A 49 588 doi: 10.1103/PhysRevA.49.588

    CrossRef Google Scholar

    [38]
    Papadopoulous G J and Hadjiagapiou I 1999 Phys. Rev. A 59 3127 doi: 10.1103/PhysRevA.59.3127

    CrossRef Google Scholar

    [39]
    Shao Z Q et al. 2014 J. Chem. Phys. 141 224110 doi: 10.1063/1.4903178

    CrossRef Google Scholar

    [40]
    Lai M Y et al. 2016 Physica A 453 305 doi: 10.1016/j.physa.2016.02.001

    CrossRef Google Scholar

    [41]
    Hanke A and Zwerger W 1995 Phys. Rev. E 52 6875 doi: 10.1103/PhysRevE.52.6875

    CrossRef Google Scholar

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