A non-Markovian Dissipative Maryland Model

TL;DR

This paper explores a non-Markovian extension of the Maryland model, linking quantum dissipation with memory effects, and analyzing how the divisibility of quantum maps relates to the process's memory.

Contribution

It introduces a non-Markovian version of the Maryland model and investigates the connection between map divisibility and memory effects in dissipative quantum dynamics.

Findings

Established a framework for non-Markovian quantum dissipative Maryland model

Linked divisibility of quantum maps to the degree of memory in the process

Provided explicit analysis of quantum memory effects in the model

Abstract

The so-called Maryland model is a linear version of the quantum kicked rotor; it exhibits Anderson localization in momentum space. By turning the kicks into a Markovian stochastic process, the dynamics becomes a dissipative quantum process described by a discrete family of completely positive maps that allows to explicitly study the relation between divisibility of the maps and the degree of memory of the process.