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On the relationship betweenT 1 andT 2 for stochastic relaxation models

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Abstract

We consider the relaxation dynamics of two quantum levels coupled to a stochastic bath. We emphasize that even if the matrix elements of the fluctuating Hamiltonian are Gaussian, a second-order cumulant truncation is not exact. For various stochastic models, including the case of a spin-1/2 particle in a fluctuating magnetic field, we calculate 1/T 1, the population relaxation rate, and 1/T 2, the phase relaxation rate, up to fourth order in perturbation theory. We show that unlike the commonly accepted second-order result that 1/T 2⩾1/2T 1, when fourth-order terms are included, in some instances 1/T 2<1/2T 1.

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Author notes

  1. J. L. Skinner

    Present address: Department of Chemistry, Columbia University, 10027, New York, New York

Authors and Affiliations

  1. Department of Chemistry, Columbia University, 10027, New York, New York

    J. Budimir

  2. Institute for Theoretical Physics, University of California, 93106, Santa Barbara, California

    J. L. Skinner

Authors
  1. J. Budimir
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  2. J. L. Skinner
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Budimir, J., Skinner, J.L. On the relationship betweenT 1 andT 2 for stochastic relaxation models. J Stat Phys 49, 1029–1042 (1987). https://doi.org/10.1007/BF01017558

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  • DOI: https://doi.org/10.1007/BF01017558

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