Efficient determination of the Markovian time-evolution towards a steady-state of a complex open quantum system

TL;DR

This paper presents a novel, exact method for solving the Markovian dynamics of complex open quantum systems described by the Nakajima-Zwanzig master equation, enabling efficient analysis of their steady states and time evolution.

Contribution

A new approach that maps the generalized master equation from Fock space to Liouville space, allowing exact eigenvalue solutions for complex quantum systems.

Findings

Successfully applied to a nano-scale electron transport system in a photon cavity.

Able to handle diverse relaxation times spanning many orders of magnitude.

Provides detailed insights into steady-state and transient behaviors.

Abstract

Master equations are commonly used to describe time evolution of open systems. We introduce a general method for calculating a Markovian solution of the Nakajima-Zwanzig generalized master equation. We do so for a time dependent transport of interacting electrons through a complex nano scale system in a photon cavity. The central system, described by 120 many-body states in a Fock space, is weakly coupled to the external leads. The very diverse relaxation times of the open system, reflecting radiative or non-radiative transitions, require information about the time evolution through many orders of magnitude. In our approach, the generalized master equation is mapped from a many-body Fock space of states to a Liouville space of transitions. We show that this results in a linear equation which is solved exactly through an eigenvalue analysis, which supplies information on the steady state and the time evolution of the system.