Quantum jumps on Anderson attractors

TL;DR

This paper explores how specific non-Hermitian dissipators influence quantum particle dynamics in disordered systems, revealing regimes of localization, diffusion, and ballistic transport with distinct jump statistics.

Contribution

It demonstrates that phase-controlled non-Hermitian dissipators can induce localization or ballistic regimes, providing new insights into quantum dynamics under dissipation.

Findings

Quantum jumps exhibit power-law statistics in diffusive regime.

Ballistic regime shows non-monotonous jump probability distribution.

Hermitian dephasing restores normal diffusion and Poissonian jumps.

Abstract

In a closed single-particle quantum system, spatial disorder induces Anderson localization of eigenstates and halts wave propagation. The phenomenon is vulnerable to interaction with environment and decoherence, that is believed to restore normal diffusion. We demonstrate that for a class of experimentally feasible non-Hermitian dissipators, which admit signatures of localization in asymptotic states, quantum particle opts between diffusive and ballistic regimes, depending on the phase parameter of dissipators, with sticking about localization centers. In diffusive regime, statistics of quantum jumps is non-Poissonian and has a power-law interval, a footprint of intermittent locking in Anderson modes. Ballistic propagation reflects dispersion of an ordered lattice and introduces a new timescale for jumps with non-monotonous probability distribution. Hermitian dephasing dissipation makes localization features vanish, and Poissonian jump statistics along with normal diffusion are recovered.