General non-Markovian dynamics of open quantum systems

TL;DR

This paper develops a comprehensive theory for non-Markovian dynamics in open quantum systems, linking exact master equations with Green functions, and explaining phenomena like non-exponential decay and oscillations due to environmental effects.

Contribution

It introduces a general framework connecting master equations with Green functions, fully accounting for environmental back-actions in non-Markovian quantum dynamics.

Findings

Non-exponential decay caused by self-energy discontinuities

Dissipationless oscillations from spectral band gaps

Exact solutions reveal environmental influence on dynamics

Abstract

We present a general theory of non-Markovian dynamics for open quantum systems. We explore the non-Markovian dynamics by connecting the exact master equations with the non-equilibirum Green functions. Environmental back-actions are fully taken into account. The non-Markovian dynamics consists of non-exponential decays and dissipationless oscillations. Non-exponential decays are induced by the discontinuity in the imaginary part of the self-energy corrections. Dissipationless oscillations arise from band gaps or the finite band structure of spectral densities. The exact analytic solutions for various non-Markovian environments show that the non-Markovian dynamics can be largely understood from the environmental-modified spectra of the open systems.