On the Lyapunov-Perron reducible Markovian Master Equation

TL;DR

This paper develops a Markovian Master Equation for open quantum systems with quasiperiodic Hamiltonians, extending previous periodic results, and analyzes stability and steady states in the weak coupling limit.

Contribution

It generalizes the construction of Markovian Master Equations to quasiperiodic systems under Lyapunov-Perron reducibility, providing new insights into their stability and steady states.

Findings

Constructed Markovian Master Equation for quasiperiodic systems

Proved CP-divisibility of the evolution in weak coupling limit

Analyzed stability and existence of quasiperiodic steady states

Abstract

We consider an open quantum system in $M_{d}(\mathbb{C})$ governed by quasiperiodic Hamiltonian with rationally independent frequencies and under assumption of Lyapunov-Perron reducibility of associated Schroedinger equation. We construct the Markovian Master Equation and resulting CP-divisible evolution in weak coupling limit regime, generalizing our previous results from periodic case. The analysis is conducted with application of projection operator techniques and concluded with some results regarding stability of solutions and existence of quasiperiodic global steady state.