Nonequilibrium quantum dissipation in spin-fermion systems

Dissipative processes in nonequilibrium 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 nonequilibrium dynamics is reflected by an exponential relaxation at long times and via complex phase shifts, leading in some cases to an “antiorthogonality” effect. In the limit of strong system-lead coupling at zero temperature we demonstrate the onset of a Marcus-like Gaussian decay with 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 nonequilibrium electronic case. The two models also differ by the orthogonality-catastrophe factor existing in a fermionic system, which modifies the resulting line shapes. Implications for current characteristics are discussed. We demonstrate the violation of pairwise Coulomb gas behavior for strong coupling to the leads. The results presented in this paper form the basis of an exact, nonperturbative description of steady-state quantum dissipative systems.