Boundary interactions changing operators and dynamical correlations in quantum impurity problems

TL;DR

This paper introduces boundary interactions changing operators within integrable quantum field theories to compute non-equilibrium dynamical correlators in quantum impurity problems, providing new exact results for occupation probabilities.

Contribution

It develops a novel axiomatic approach to handle boundary interactions changing operators, enabling the calculation of non-equilibrium correlators in quantum impurity models.

Findings

Derived exact large-time behavior of occupation probability P(t)

Found universal ratio for oscillation frequency and decay rate

Extended integrable quantum field theory methods to non-equilibrium scenarios

Abstract

Recent developments have made possible the computation of equilibrium dynamical correlators in quantum impurity problems. In many situations however, one is rather interested in correlators subject to a non equilibrium initial preparation; this is the case for instance for the occupation probability $P(t)$ in the double well problem of dissipative quantum mechanics (DQM). We show in this paper how to handle this situation in the framework of integrable quantum field theories by introducing ``boundary interactions changing operators''. We determine the properties of these operators by using an axiomatic approach similar in spirit to what is done for form-factors. This allows us to obtain new exact results for $P(t)$; for instance, we find that that at large times (or small $g$), the leading behaviour for $g < 1/2}$ is $P(t)\propto e^{-\Gamma t}\cos\Omega t$, with the universal ratio. $\Omega/\Gamma = \cot {\pi g}/{2(1-g)}$.