The fast recurrent subspace on an $N$-level quantum energy transport model

TL;DR

This paper characterizes the structure of invariant states and their spectra in an N-level quantum energy transport model, revealing the dynamics and long-term behavior of the system using a generalized Fourier transform.

Contribution

It introduces a novel analysis of the invariant states and their spectra for a quantum transport model using a generalized Fourier transform, advancing understanding of quantum Markov semigroups.

Findings

Identification of the fast recurrent subspace as the support of invariant states

Spectral characterization of invariant states via a generalized Fourier transform

Analysis of the system's long-time behavior and attraction domains

Abstract

The fast recurrent subspace (the biggest support of all invariant states) of a Weak Coupling Limit Type Quantum Markov Semigroup modeling a quantum transport open system of $N$-energy levels is determined. This is achieved by characterizing the structure of all the invariant state and their spectra in terms of a natural generalization of the Discrete Fourier Transform operator. Finally, the attraction domains and long-time behavior of the evolution are studied on hereditary subalgebras where faithful invariant states exist.