Numerical Evidence for Approximate Consistency and Markovianity of some Quantum Histories in a Class of Finite Closed Spin Systems

TL;DR

This paper provides numerical evidence that certain quantum spin systems exhibit approximate classical Markovian behavior under specific conditions, bridging quantum dynamics and classical stochastic processes.

Contribution

It demonstrates, through numerical simulations, that the conditions for approximate classical consistency and Markovianity are well satisfied in finite quantum spin systems, especially as system size grows.

Findings

Conditions for classical Markovianity are approximately fulfilled in spin models.

Accuracy of classical approximation improves with system size.

Numerical evidence supports the quantum-to-classical transition in these systems.

Abstract

Closed quantum systems obey the Schroedinger equation whereas nonequilibrium behavior of many of systems is routinely described in terms of classical, Markovian stochastic processes. Evidently, there are fundamental differences between those two types of behavior. We discuss the conditions under which the unitary dynamics may be mapped onto pertinent classical stochastic processes. This is first principally addressed based on the notions of "consistency" and "Markovianity." Numerical data are presented that show that the above conditions are to good approximation fulfilled for Heisenberg-type spin models comprising 12-20 spins. The accuracy to which these conditions are met increases with system size.