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Exponentially damped operators for a harmonic oscillator linearly coupled to a heat bath

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Abstract

We consider the problem of the dissipative dynamics of a harmonic oscillator linearly coupled to a heat bath. We demonstrate that in addition to the mean energy, there exists an infinite series of quantities exponentially decreasing in time that are means of polynomials of the system Hamiltonian. We obtain the spectrum of the corresponding relaxation times. We propose a method for representing the time characteristics of the system in terms of operators corresponding to the exponentially damped observables. We obtain a recurrence relation for these operators.

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Correspondence to I. O. Glebov.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 162, No. 2, pp. 243–253, February, 2010.

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Glebov, I.O., Eremin, V.V. Exponentially damped operators for a harmonic oscillator linearly coupled to a heat bath. Theor Math Phys 162, 201–210 (2010). https://doi.org/10.1007/s11232-010-0015-5

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Keywords

  • quantum theory of dissipation
  • Redfield theory
  • reduced density matrix
  • correlation function matrix
  • harmonic oscillator