Coherence correlations in the dissipative two-state system

Details Coherence correlations in the dissipative two-state system Coherence correlations in the dissipative two-state system

1998-07-17

arxiv.org/abs/cond-mat/9807252v1

Phys. Rev. E 58, 4288 (1998)

Physics

Condensed Matter

Statistical Mechanics

19 pages, 4 figures, to be published in Phys. Rev. E

Scientific paper

10.1103/PhysRevE.58.4288

We study the dynamical equilibrium correlation function of the polaron-dressed tunneling operator in the dissipative two-state system. Unlike the position operator, this coherence operator acts in the full system-plus-reservoir space. We calculate the relevant modified influence functional and present the exact formal expression for the coherence correlations in the form of a series in the number of tunneling events. For an Ohmic spectral density with the particular damping strength $K=1/2$, the series is summed in analytic form for all times and for arbitrary values of temperature and bias. Using a diagrammatic approach, we find the long-time dynamics in the regime $K<1$. In general, the coherence correlations decay algebraically as $t^{-2K}$ at T=0. This implies that the linear static susceptibility diverges for $K\le 1/2$ as $T\to 0$, whereas it stays finite for $K>1/2$ in this limit. The qualitative differences with respect to the asymptotic behavior of the position correlations are explained.

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