Diffusive transport from spatially correlated random phase kicks

TL;DR

This paper investigates how spatially correlated random phase kicks affect quantum transport in a one-dimensional lattice, revealing a transition from ballistic to diffusive behavior with explicit diffusion coefficients.

Contribution

It introduces a controllable model of dephasing with finite spatial correlation, deriving an analytical expression for the diffusion coefficient based on phase noise structure.

Findings

Phase kicks suppress ballistic transport and induce diffusion.

Derived explicit formula for diffusion coefficient as a function of correlation length.

Numerical simulations confirm analytical predictions.

Abstract

We study the dynamics of a single-particle wave packet on a one-dimensional lattice subject to periodic random phase kicks with finite spatial correlation length. This stroboscopic setting provides a controllable model of dephasing in driven quantum systems. Using a momentum-space formulation, we show that the evolution is governed by an accumulated phase whose structure determines the spreading of the wave packet. We find that the phase kicks strongly suppress ballistic transport and induce diffusion at long times. We derive an explicit analytical expression for the diffusion coefficient as a function of the correlation length, in excellent agreement with numerical simulations. Our results uncover a simple mechanism by which spatially correlated phase noise controls quantum transport, and provide a quantitatively testable prediction for diffusion in periodically driven lattice systems. Possible experimental realizations in cold-atom platforms are discussed.