Localization in active incommensurate arrays

TL;DR

This paper investigates how dissipation, energy pumping, and nonlinearity affect localization and phase transitions in incommensurate arrays, revealing thresholds and transition behaviors distinct from disordered systems.

Contribution

It extends the understanding of localization by including dissipation and nonlinearity, identifying a finite excitation threshold and phase transition features in incommensurate arrays.

Findings

Finite excitation threshold in metallic and insulating regimes

Second order phase transition to global oscillations observed

Anderson attractor regime appears only in strong localization limit

Abstract

In a dissipationless linear lattice, spatial disorder or incommensurate modulation induce localization of the lattice eigenstates and block spreading of wave packets. Additionally, incommensurate arrays allow for the metal-insulator transition at a finite modulation amplitude already in one dimension. The addition of nonlinearity to the lattice Hamiltonian causes interaction between the eigenstates, which results in a slow packet spreading. We go beyond the dissipationless limit and consider nonlinear quasi-periodic arrays that are subjected to the dissipative losses and energy pumping. We find that there is a finite excitation of oscillations threshold in both metallic and insulating regimes. Moreover, excitation in the metallic and weakly insulating regime displays features of the second order phase transition to global oscillations, in contrast to disordered arrays. The Anderson attractor regime is recovered only in the limit of strong localization. The identified transition, and the further onset of chaos and synchronization can be potentially realized with polariton condensates lattices and cavity-QED arrays.