Non-exponential decay in classical stochastic processes with memory

TL;DR

This paper investigates how classical stochastic processes with memory exhibit non-exponential, quadratic initial decay, contrasting with quantum systems, and explores the implications of noise with memory on transition dynamics.

Contribution

It demonstrates that classical processes with memory can produce quadratic initial decay, providing insights into the differences between classical and quantum decay behaviors.

Findings

Classical stochastic processes with memory show quadratic initial decay.

Memory in noise influences the transition dynamics.

Quantum decay cannot be slowed by quadratic initial behavior.

Abstract

The initial time-dependence of a state in circumstances where it makes transitions to, or decay to, a second state has been investigated. In classical stochastic processes, the observed time dependence of transition or decay proportional to $t^2$ is attributed to the noise with memory. In contrast to quantum mechanics, the quadratic form of initial decay is unable to decelerate the evolution of the system.