Equilibrium dynamics of the dissipative two-state system

TL;DR

This paper uses renormalization group methods to analyze the dynamics of the dissipative two-state system by mapping it onto the anisotropic Kondo model, revealing a crossover between different dissipation regimes.

Contribution

It demonstrates that the anisotropic Kondo model accurately describes the dissipative two-state system's dynamics across a range of dissipation strengths.

Findings

The AKM captures the physics for dissipation strength 0 to 4.

Identifies a smooth crossover between weak and strong dissipation regimes.

Provides a detailed dynamical analysis using renormalization group techniques.

Abstract

Wilson's momentum shell renormalization group method is used to solve for the dynamics of the dissipative two--state system. We utilize the mapping of the spin--boson model onto the anisotropic Kondo model (AKM) and solve for the dynamics of the latter. We find that the AKM captures the physics of the dissipative two--state system for dissipation strength $0\leq\alpha\leq 4$ corresponding to $\infty\geq J_{\parallel}\geq -\infty$ in the AKM. The dynamics of the AKM shows a smooth crossover between two strong coupling regimes corresponding to weak and strong dissipation in the spin--boson model.