From Classical to quantum stochastic process

TL;DR

This paper introduces a method to construct quantum analogs of classical stochastic processes by replacing path decisions with superpositions, revealing how quantum coherence can alter dynamics and potentially accelerate relaxation.

Contribution

It presents a novel approach to derive quantum analogs from classical stochastic processes, highlighting the impact of coherence on scaling behavior and domain growth.

Findings

Quantum analogs exhibit different domain growth exponents.

Coherence can accelerate the relaxation process.

Quantum effects can alter classical scaling laws.

Abstract

In this paper for the first time, we construct quantum analogs starting from classical stochastic processes, by replacing random which path decisions with superpositions of all paths. This procedure typically leads to non-unitary quantum evolution, where coherences are continuously generated and destroyed. In spite of their transient nature, these coherences can change the scaling behavior of classical observables. Using the zero temperature Glauber dynamics in a linear Ising spin chain, we find quantum analogs with different domain growth exponents. In some cases, this exponent is even smaller than for the original classical process, which means that coherence can play an important role to speed up the relaxation process.