Dynamics of a Strongly Damped Two-Level System: Beyond the DBGA

TL;DR

This paper investigates the dissipative two-level system dynamics beyond the dilute bounce gas approximation, revealing deviations at low temperatures and a crossover in relaxation behavior in the Kondo regime, with implications for quantum Zeno effects.

Contribution

It introduces a quantum relaxation theory calculation that surpasses the dilute bounce gas approximation for strong damping, providing new insights into low-temperature dynamics and Kondo regime behavior.

Findings

Deviations from DBGA at low temperatures.

Identification of a crossover to slower exponential relaxation.

Agreement with conformal field theory results in the Kondo regime.

Abstract

Dynamics of a dissipative two-level system is studied using quantum relaxation theory. This calculation for the first time goes beyond the commonly used dilute bounce gas approximation (DBGA), even for strong damping. The new results obtained here deviate from the DBGA results at low temperatures, however, the DBGA form is recovered at high temperatures. The results in the parameter regime $ 1/2<\alpha <1$, where the model has connection with the Kondo Hamiltonian, are of particular significance. In this regime, the spin shows a cross-over to a slower exponential relaxation at intermediate times, which is roughly half the relaxation rate at short times, as also observed in Quantum Monte-Carlo simulation of the model. The asymptotic behavior of the spin in the Kondo regime is in agreement with the exact conformal field theory results for the Kondo model. A connection of the dissipative dynamics of the two-level system with the quantum Zeno effect is also presented.