Diffusion in disordered systems under iterative measurement

TL;DR

This paper investigates how repeated measurements affect quantum diffusion in disordered systems, revealing a transition from localization to diffusion and the emergence of the Quantum Zeno effect.

Contribution

It analytically connects measurement sequences with diffusion behavior and shows how decoherence can overcome Anderson localization.

Findings

Diffusive regime occurs under rapid measurements

Diffusion coefficient D is analytically derived

Quantum Zeno effect observed as D approaches zero

Abstract

We consider a sequence of idealized measurements of time-separation $\Delta t$ onto a discrete one-dimensional disordered system. A connection with Markov chains is found. For a rapid sequence of measurements, a diffusive regime occurs and the diffusion coefficient $D$ is analytically calculated. In a general point of view, this result suggests the possibility to break the Anderson localization due to decoherence effects. Quantum Zeno effect emerges because the diffusion coefficient $D$ vanishes at the limit $\Delta t \to 0$.