Decay of correlations in the dissipative two-state system

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 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 proportional to 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.