Boundary Interaction 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 interested in correlators subject to a nonequilibrium initial preparation. This is the case, for instance, for the occupation probability $P(t)$ in the double well problem of dissipative quantum mechanics. We show here how to handle this situation in the framework of integrable quantum field theories. This allows us to obtain new exact results for $P(t)$: for instance, we find that at large times (or small $g$), the leading behavior for $g<\frac{1}{2}$ is $P(t)\ensuremath{\propto}{e}^{\ensuremath{-}\ensuremath{\Gamma}t}\mathrm{cos}\ensuremath{\Omega}t$, with the universal ratio $\frac{\ensuremath{\Omega}}{\ensuremath{\Gamma}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\mathrm{cot}\frac{\ensuremath{\pi}g}{2(1\ensuremath{-}g)}$.