A rigorous derivation of the transition rate for the dissipative two-state system

TL;DR

This paper provides a rigorous derivation of the transition rate for a dissipative two-state quantum system interacting with a heat bath, improving upon previous formal methods by using a quantum resonance approach.

Contribution

It introduces a mathematically rigorous derivation of the transition rate, extending prior formal results with a resonance-based method.

Findings

Derivation confirms the form of the transition rate for small tunneling.

Uses quantum resonance approach for rigorous analysis.

Results align with previous formal derivations.

Abstract

The transition rate for a two-state system interacting with a bosonic heat bath, from the initial state `up' at time t=0 to `down' at time t>0, was derived formally in the seminal paper [12] by Leggett, Chakravarty, Dorsey, Fisher, Garg and Zwerger. The expression was obtained for small tunneling parameter of the two-level system using time-dependent perturbation theory to second order. It contains all orders in the parameter of coupling between the system and the bath. We give a rigorous derivation of the transition rate, using a quantum resonance approach.