Non-Equilibrium Quantum Dissipation

TL;DR

This paper investigates non-equilibrium quantum dissipation in a spin-fermion model, revealing complex relaxation dynamics, voltage-activated decay, and differences from equilibrium models, providing a basis for exact non-perturbative analysis.

Contribution

It offers a detailed non-perturbative analysis of non-equilibrium quantum dissipation in a spin-fermion system, highlighting new decay behaviors and the impact of strong coupling.

Findings

Exponential relaxation with phase shifts and anti-orthogonality effects.

Voltage difference induces Marcus-like Gaussian decay at strong coupling.

Violation of pair-wise Coulomb gas behavior at strong lead coupling.

Abstract

Dissipative processes in non-equilibrium many-body systems are fundamentally different than their equilibrium counterparts. Such processes are of great importance for the understanding of relaxation in single molecule devices. As a detailed case study, we investigate here a generic spin-fermion model, where a two-level system couples to two metallic leads with different chemical potentials. We present results for the spin relaxation rate in the nonadiabatic limit for an arbitrary coupling to the leads, using both analytical and exact numerical methods. The non-equilibrium dynamics is reflected by an exponential relaxation at long times and via complex phase shifts, leading in some cases to an "anti-orthogonality" effect. In the limit of strong system-lead coupling at zero temperature we demonstrate the onset of a Marcus-like Gaussian decay with {\it voltage difference} activation. This is analogous to the equilibrium spin-boson model, where at strong coupling and high temperatures the spin excitation rate manifests temperature activated Gaussian behavior. We find that there is no simple linear relationship between the role of the temperature in the bosonic system and a voltage drop in a non-equilibrium electronic case. The two models also differ by the orthogonality-catastrophe factor existing in a fermionic system, which modifies the resulting lineshapes. Implications for current characteristics are discussed. We demonstrate the violation of pair-wise Coulomb gas behavior for strong coupling to the leads. The results presented in this paper form the basis of an exact, non-perturbative description of steady-state quantum dissipative systems.