Proximity-measurement induced random localization in quantum fluids

TL;DR

This paper investigates how post-selected proximity measurements cause partial and eventual full localization of particles in a quantum fluid, revealing a scaling behavior in the distribution of localization lengths.

Contribution

It introduces a model showing how random proximity measurements induce localization while maintaining macroscopic homogeneity in quantum fluids.

Findings

Partial localization of particles occurs due to measurements.

All particles eventually localize with a distribution of lengths.

Localization length distribution follows a known scaling form.

Abstract

Proximity measurements probe whether pairs of particles are close to one another. We consider the impact of post-selected random proximity measurements on a quantum fluid of many distinguishable particles. We show that such measurements induce random spatial localization of a fraction of the particles, and yet preserve homogeneity macroscopically. Eventually, all particles localize, with a distribution of localization lengths that saturates at a scale controlled by the typical measurement rate. The steady-state distribution of these lengths is governed by a familiar scaling form.