Time-convolutionless master equation for mesoscopic electron-phonon systems

TL;DR

This paper derives a time-convolutionless master equation for electron-phonon systems that remains valid beyond the golden rule approximation, revealing recurrence phenomena and complex relaxation behaviors in mesoscopic models.

Contribution

It introduces a general formalism for the time-convolutionless master equation applicable to mesoscopic electron-phonon systems, capturing non-exponential relaxation and recurrence effects.

Findings

Relaxation deviates from simple exponential decay in mesoscopic systems.

Recurrence phenomena appear on slow mode time-scales.

Numerical simulations confirm complex relaxation dynamics in various models.

Abstract

The time-convolutionless master equation for the electronic populations is derived for a generic electron-phonon Hamiltonian. The equation can be used in the regimes where the golden rule approach is not applicable. The equation is applied to study the electronic relaxation in several models with the finite number normal modes. For such mesoscopic systems the relaxation behavior differs substantially from the simple exponential relaxation. In particular, the equation shows the appearance of the recurrence phenomena on a time-scale determined by the slowest mode of the system. The formal results are quite general and can be used for a wide range of physical systems. Numerical results are presented for a two level system coupled to Ohmic and super-Ohmic baths, as well as for a model of charge-transfer dynamics between semiconducting organic polymers.