Coherence correlations in the dissipative two-state system

TL;DR

This paper investigates the dynamical coherence correlations in a dissipative two-state quantum system, deriving exact expressions and analyzing their long-time behavior, revealing critical damping effects and divergence conditions at zero temperature.

Contribution

It provides an exact series expression for coherence correlations and analyzes their decay, highlighting differences from position correlations and the impact of damping strength.

Findings

Coherence correlations decay algebraically as t^{-2K} at T=0.

Divergence of static susceptibility occurs for K ≤ 1/2 as T approaches zero.

Exact analytic summation of the series for K=1/2 across all times.

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.