Coherent-incoherent transition and relaxation in condensed-phase tunneling systems

C. H. Mak and David Chandler
Phys. Rev. A 44, 2352 – Published 1 August 1991
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Abstract

The tunneling dynamics of the spin-boson problem has been computed using discretized path-integral simulations for temperatures T and couplings, i.e., the Kondo parameter α, spanning the entire T-α plane. The inherent problem of alternating weights has been solved using a combination of the stationary-phase Monte Carlo method and contour-distortion techniques. A transition from coherent to purely incoherent relaxation was observed for the spin correlation function. The time correlation functions and the location of the coherent-incoherent boundary on the T-α plane are well described by the noninteracting-blip approximation. In the deep-tunneling limit of large α, low T, and high bath frequency, the system relaxes exponentially, with its relaxation time constant following a power-law temperature dependence, in accord with perturbation theory. At higher T and low bath frequency, the relaxation time crosses over to a classical Arrhenius temperature dependence, reflecting the onset of activated processes. For a narrow region within 1/2<α<1, numerical results suggest that the system undergoes incoherent relaxation, with a short-time exponential decay, followed by a long-time tail of the power-law type. The short-time exponential relaxation time follows a peculiar power-law temperature dependence, with the relaxation rate increasing as a function of decreasing temperature.

  • Received 15 April 1991

DOI:https://doi.org/10.1103/PhysRevA.44.2352

©1991 American Physical Society

Authors & Affiliations

C. H. Mak and David Chandler

  • Department of Chemistry, University of California, Berkeley, California 94720

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Issue

Vol. 44, Iss. 4 — August 1991

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