Phase transitions of wave packet dynamics in disordered non-Hermitian systems

TL;DR

This paper explores how disorder affects wave packet dynamics in non-Hermitian systems, revealing unique phase transitions with different critical exponents and behaviors compared to Hermitian counterparts.

Contribution

It uncovers new dynamical phase transitions in disordered non-Hermitian systems, highlighting differences from traditional Anderson localization.

Findings

Disorder induces localization and unidirectional amplification.

Transitions between localized and propagating phases occur with a critical exponent of 1/2.

Wave packet dynamics differ fundamentally from Hermitian systems due to lack of energy conservation.

Abstract

Disorder can localize the eigenstates of one-dimensional non-Hermitian systems, leading to an Anderson transition with a critical exponent of 1. We show that, due to the lack of energy conservation, the dynamics of individual, real-space wave packets follows a different behavior. Both transitions between localization and unidirectional amplification, as well as transitions between distinct propagating phases become possible. The critical exponent of the transition equals $1/2$ in propagating-propagating transitions.