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An equation for the quantum dissipative system in statistical mechanics

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Abstract

A formalism for describing quantum dissipative systems in statistical mechanics is developed. A new equation of the Lindblad type with a quadratic superoperator consisting of Hermitian dissipative operators is derived from the Bloch equation for temperature density matrix using the Feynman integral over the trajectories with a modified Menskii weight functional. By way of example, this equation is solved for a one-dimensional quantum harmonic oscillator with linear dissipation. Applying the projection operator technique, an integral-differential equation for a reduced temperature statistical operator is obtained, which is analogous to the Zwanzig equation in statistical mechanics, and its formal solution is found as a convergent series.

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References

  1. R. Feynman, Statistical Mechanics, Addison-Wesley, 1972.

  2. M. B. Menskii, Quantum Measurements and Decoherenization [in Russian], Fiz. Mat. Literat, Moscow, 2001.

    Google Scholar 

  3. M. B. Menskii, Usp. Fiz. Nauk, 173, No. 11, 1199 (2003).

    Article  Google Scholar 

  4. R. L. Stratonovich, Phys. A, 236, 335 (1997).

    Article  Google Scholar 

  5. G. Lindblad, Commun. Math. Phys., 48, No. 2, 119 (1976).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  6. R. L. Zwanzig, J. Chem. Phys., 33, 1388 (1960).

    Article  Google Scholar 

  7. G. Dyoch, A Manual to Practical Application of the Laplace and Z Conversion [in Russian], Nauka, Moscow, 1971.

    Google Scholar 

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Authors and Affiliations

  1. Perm State Technical University, Perm

    V. S. Kirchanov

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  1. V. S. Kirchanov
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 30–34, December, 2006.

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Kirchanov, V.S. An equation for the quantum dissipative system in statistical mechanics. Russ Phys J 49, 1294–1300 (2006). https://doi.org/10.1007/s11182-006-0258-7

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  • DOI: https://doi.org/10.1007/s11182-006-0258-7

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