Transition maps between Hilbert subspaces and quantum energy transport

TL;DR

This paper introduces transition maps between Hilbert subspaces using a generalized Fourier transform, extending quantum energy transport models and analyzing invariant states in open quantum systems.

Contribution

It presents a novel method of defining transition maps as Kraus operators, extending existing quantum energy transport models to include new structural insights.

Findings

Derived the structure of invariant states in the extended model

Demonstrated the use of transition maps as noise operators

Extended the quantum energy transport framework

Abstract

We use a natural generalization of the discrete Fourier transform to define transition maps between Hilbert subspaces and the global transport operator $Z$. By using these transition maps as Kraus (or noise) operators, an extension of the quantum energy transport model of 10.1142/S0219025718500182 describing the dynamics of an open quantum system of $N$-levels is presented. We deduce the structure of the invariant states which can be recovered by transporting states supported on the first level.