Decay of correlations in the dissipative two-state system

TL;DR

This paper analyzes the decay of correlations in a dissipative two-state quantum system, providing exact and asymptotic results for correlation functions across different parameters, revealing distinct decay behaviors linked to interaction types.

Contribution

It offers analytic solutions for correlation functions at all times for specific damping strengths and characterizes their asymptotic decay laws, advancing understanding of dissipative quantum dynamics.

Findings

Correlation functions are analytically derived for all times at K=1/2.

At T=0, tunneling correlations decay as t^{-2K}.

Position correlations universally decay as t^{-2}.

Abstract

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.