Boundary interactions changing operators and dynamical correlations in quantum impurity problems

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 $P(t)\propto e^{-Γt}\cosΩt$, with the universal ratio. $Ω/Γ= \cot {πg}/{2(1-g)}$.