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Connection between the Schrödinger equation for dissipative systems and the master equation

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  • Caldirola, P.
  • Lugiato, L.A.

Abstract

We study the relations between the Caldirola-Kanai (C-K) description of friction in quantum mechanics and the fundamental master equation (ME) approach. The original C-K equation is shown to be equivalent to a ME without fluctuation term. In the case of the damped harmonic oscillator, the C-K equation with stochastic potential turns out to be equivalent to the complete ME. The formulation in terms of Wigner function is also worked out.

Suggested Citation

  • Caldirola, P. & Lugiato, L.A., 1982. "Connection between the Schrödinger equation for dissipative systems and the master equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 116(1), pages 248-264.
    • Handle: RePEc:eee:phsmap:v:116:y:1982:i:1:p:248-264
    DOI: 10.1016/0378-4371(82)90242-4
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    1. Micheline Thomine-Desmazures, 1965. "L'investigation psychosociologique en milieu rural," Économie rurale, Programme National Persée, vol. 64(1), pages 19-24.
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    Cited by:

    1. Eckhardt, W., 1987. "On the consistent description of quantum relaxation processes: The harmonic oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 141(1), pages 81-110.
    2. Yannouleas, C., 1985. "Quantal Brownian motion from RPA dynamics: The master and Fokker-Planck equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 132(1), pages 1-27.

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