Coherence correlations in the dissipative two-state system

Abstract

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.

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

References in corpus (3)

• Dynamical simulation of current fluctuations in a dissipative two-state system
• Boundary interactions changing operators and dynamical correlations in quantum impurity problems
• Scaling and universality in the anisotropic Kondo model and the dissipative two-state system

Cited by in corpus (4)

• Quantum dynamics of the dissipative two-state system coupled with a sub-Ohmic bath
• Random Lindblad equations from complex environments
• Quantum regression theorem for non-Markovian Lindblad equations
• Decoherence and relaxation of qubits coupled to low- and medium-frequency Ohmic baths directly and via a harmonic oscillator