Classical Diffusion of a quantum particle in a noisy environment

TL;DR

This paper investigates how quantum wavepackets in a noisy environment transition to classical diffusion, providing analytical expressions for the diffusion coefficient based on noise characteristics, applicable across various physical systems.

Contribution

It introduces a general analytical approach to describe the emergence of classical diffusion from quantum dynamics in noisy environments with finite correlation times.

Findings

Classical diffusion emerges at long times due to decoherence.

Analytical dependence of diffusion coefficient on noise magnitude and correlation time.

Applicable to electronic transport, optical transmission, exciton diffusion, and quantum computing.

Abstract

We study the spreading of a quantum-mechanical wavepacket in a one-dimensional tight-binding model with a noisy potential, and analyze the emergence of classical diffusion from the quantum dynamics due to decoherence. We consider a finite correlation time of the noisy environment, and treat the system by utilizing the separation of fast (dephasing) and slow (diffusion) processes. We show that classical diffusive behavior emerges at long times, and we calculate analytically the dependence of the classical diffusion coefficient on the noise magnitude and correlation time. This method provides a general solution to this problem for arbitrary conditions of the noisy environment. The results are relevant to a large variety of physical systems, from electronic transport in solid state physics, to light transmission in optical devices, diffusion of excitons, and quantum computation.