Quantum quenches and driven dynamics in a single-molecule device

TL;DR

This paper provides an exact analytical solution for the nonequilibrium dynamics of a single-molecule device under quantum quenches and ac drives, revealing detailed thermalization and relaxation behaviors.

Contribution

It introduces a controllable quadratic bosonic model for molecular devices and solves it exactly for various nonequilibrium scenarios, including quenches and driven dynamics.

Findings

System thermalizes after a local quantum quench.

Relaxation times vary depending on the observable.

Long-time oscillation amplitudes depend on drive frequency.

Abstract

The nonequilibrium dynamics of molecular devices is studied in the framework of a generic model for single-molecule transistors: a resonant level coupled by displacement to a single vibrational mode. In the limit of a broad level and in the vicinity of the resonance, the model can be controllably reduced to a form quadratic in bosonic operators, which in turn is exactly solvable. The response of the system to a broad class of sudden quenches and ac drives is thus computed in a nonperturbative manner, providing an asymptotically exact solution in the limit of weak electron-phonon coupling. From the analytic solution we are able to (1) explicitly show that the system thermalizes following a local quantum quench, (2) analyze in detail the time scales involved, (3) show that the relaxation time in response to a quantum quench depends on the observable in question, and (4) reveal how the amplitude of long-time oscillations evolves as the frequency of an ac drive is tuned across the resonance frequency. Explicit analytical expressions are given for all physical quantities and all nonequilibrium scenarios under study.