Nonequilibrium quantum decay and decoherence in quantum impurity problems

TL;DR

This paper derives exact relations and closed-form expressions for quantum decay and dephasing rates in impurity models, revealing the limitations of traditional rate approximations and elucidating the crossover from weak to strong tunneling.

Contribution

It establishes exact relations between nonequilibrium decay rates in impurity models and derives closed-form expressions for the dissipative two-state system, advancing understanding of quantum decay in these systems.

Findings

Exact relations between decay rates of boundary sine-Gordon and Kondo models.

Closed-form expressions for quantum decay rates in the dissipative two-state system.

Identification of regimes where Golden Rule approximation fails.

Abstract

Using detailed balance and scaling properties of integrals that appear in the Coulomb gas reformulation of quantum impurity problems, we establish exact relations between the nonequilibrium quantum decay rates of the boundary sine-Gordon and the anisotropic Kondo model at zero temperature. Combining these results with findings from the thermodynamic Bethe ansatz, we derive exact closed form expressions for the quantum decay rate of the dissipative two-state system in the scaling limit. These expressions illustrate how the crossover from weak to strong tunneling takes place. We trace out the regimes in which the usually applied Golden Rule (nonadiabatic) rate expression fails. Using a conjectured correspondence between the relaxation and dephasing rate, we obtain the exact lower bound of the dephasing rate as a function of bias and dissipation strength.