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Phase variable and phase relaxation processes in the Liouville space

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  • Ban, Masashi

Abstract

The quantum dissipative dynamics of a phase variable is studied. A phase variable is treated as a quantum mechanical operator in Liouville space. The time translation properties of a phase operator and its eigenstate are investigated in terms of a time-evolution generator describing the phase relaxation process. The model corresponds to a quantum mechanical generalization of the random frequency modulation. An arbitrary state of a system can be expressed in terms of superpositions of the eigenstates of a phase operator. It is found that the width of a wave packet expressed by the phase eigenstates spreads monotonously with time, and that any stationary state is a completely random phase state. Such a phase randomizing process makes the entropy of a system increase. This process is also discussed with regard to stochastic processes. The Langevin equation for the phase variable and the Fokker-Planck equation for the probability distribution function in the phase eigenspace are obtained.

Suggested Citation

  • Ban, Masashi, 1991. "Phase variable and phase relaxation processes in the Liouville space," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 179(1), pages 103-130.
    • Handle: RePEc:eee:phsmap:v:179:y:1991:i:1:p:103-130
    DOI: 10.1016/0378-4371(91)90217-Z
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    References listed on IDEAS

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    1. Arimitsu, T. & Pradko, J. & Umezawa, H., 1986. "Generating functional methods in non-equilibrium thermo field dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 135(2), pages 487-504.
    2. Ban, Masashi & Arimitsu, Toshihico, 1985. "A solvable model of microscopic frequency modulation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 129(3), pages 455-468.
    3. Arimitsu, T. & Sudo, Y. & Umezawa, H., 1987. "Dynamical rearrangement of the thermal vacuum in thermo field dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 146(3), pages 433-451.
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