Localization due to topological stochastic disorder in active networks

TL;DR

This paper explores how topological stochastic disorder in active networks, caused by non-uniform illumination, leads to localization and complex relaxation spectra, revealing new non-Hermitian effects in non-equilibrium systems.

Contribution

It introduces the concept of topological stochastic disorder in active networks and analyzes its impact on relaxation dynamics and localization phenomena.

Findings

TSD induces non-Hermitian effects and complex spectra.

Localization significantly influences relaxation behavior.

Three routes to under-damped relaxation are identified.

Abstract

An active network is a prototype model in non-equilibrium statistical mechanics. It can represent, for example, a system with particles that have a self-propulsion mechanism. Each node of the network specifies a possible location of a particle, and its orientation. The orientation (which is formally like a spin degree of freedom) determines the self-propulsion direction. The bonds represent the possibility to make transitions: to hop between locations; or to switch the orientation. In systems of experimental interest (Janus particles), the self-propulsion is induced by illumination. An emergent aspect is the topological stochastic disorder (TSD). It is implied by the non-uniformity of the illumination. In technical terms the TSD reflects the local non-zero circulations (affinities) of the stochastic transitions. This type of disorder, unlike non-homogeneous magnetic field, is non-hermitian, and can lead to the emergence of a complex relaxation spectrum. It is therefore dramatically distinct from the conservative Anderson-type or Sinai-type disorder. We discuss the consequences of having TSD. In particular we illuminate 3~different routes to under-damped relaxation, and show that localization plays a major role in the analysis. Implications of the bulk-edge correspondence principle are addressed too.