Dynamical Behavior of the Dissipative Two-State System

TL;DR

This paper studies the dynamical behavior of a quantum two-state system coupled to a heat bath, revealing how dissipation affects coherence and damping through simulations and phase diagrams.

Contribution

It introduces a quasiparticle picture and phase diagrams for the dissipative two-state system, connecting Monte Carlo results with analytical approximations.

Findings

Transition from oscillatory to damped behavior near alpha=1/2

Biased systems have higher crossover coupling alpha_c

Phase diagrams map coherence and damping regimes

Abstract

We investigate the dynamical correlation function of a quantum-mechanical two-state system which is coupled to a bosonic heat bath, utilizing the equivalence between the spin-boson Hamiltonian and the 1/r^2 Ising model. The imaginary-time correlation function is calculated by Monte-Carlo simulations on the Ising system and then continued to real time by a Pade approximation. In the unbiased system, the transition from oscillatory to strongly damped behavior is found to occur at a coupling strength close to alpha = 1/2. The biased system favors coherent relaxation and displays a significantly larger crossover value alpha_c. We introduce the quasiparticle picture to describe the relevant behavior at intermediate time scales. Within this approximation, we map out phase diagrams for the unbiased and biased systems.