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Non-Markovian relaxation of a quantum system

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  • Cataldo, Horacio M.

Abstract

A non-Markovian treatment of the relaxation of a spin j is developed. The corresponding reduced collision operator admits a discrete spectral representation whose eginevalues are extracted in a high temperature limit. Then, assuming a phonon reservoir with a Debye-like density of phonon states, the time evolution of the collision operator is explicitly given, showing that the corresponding time decay arises from the branch points of its Laplace transform. The extraction of the analytic continuation of the transform allows the memory effects on the relaxation frequencies (resolvent poles) to be analyzed and the validity of the rotating-wave approximation to be tested.

Suggested Citation

  • Cataldo, Horacio M., 1990. "Non-Markovian relaxation of a quantum system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 165(2), pages 249-269.
    • Handle: RePEc:eee:phsmap:v:165:y:1990:i:2:p:249-269
    DOI: 10.1016/0378-4371(90)90194-W
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    References listed on IDEAS

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    1. Lindenberg, Katja & Mohanty, Udayan & Seshadri, V., 1983. "Hamiltonian model for the Brownian motion of a rigid rotor," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 119(1), pages 1-16.
    2. Kelley, Allen C., 1964. "The London Capital Market and Australia, 1870–1914. By A. R. Hall. Canberra: Australian National University Press, 1963. Pp. xiii, 221. 30s," The Journal of Economic History, Cambridge University Press, vol. 24(3), pages 399-401, September.
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