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Register a new userDecay of correlations in the dissipative two-state system
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G. Lang
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We study the equilibrium correlation function of the polaron-dressed tunnelling operator in the dissipative two-state system and compare the asymptoptic dynamics with that of the position correlations. For an Ohmic spectral density with the damping strength $K=1/2$, the correlation functions are obtained in analytic form for all times at any $T$ and any bias. For $K<1$, the asymptotic dynamics is found by using a diagrammatic approach within a Coulomb gas representation. At T=0, the tunnelling or coherence correlations drop as $t^{-2K}$, whereas the position correlations show universal decay $propto t^{-2}$. The former decay law is a signature of unscreened attractive charge-charge interactions, while the latter is due to unscreened dipole-dipole interactions.
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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 $Kle 1/2$ as $Tto 0$, 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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