# Fractality in nonequilibrium steady states of quasiperiodic systems

## TL;DR

This paper explores how boundary-driven nonequilibrium states in quasiperiodic systems reveal underlying fractal structures, with implications for understanding transport properties at criticality.

## Contribution

It demonstrates that boundary driving can probe fractality in quasiperiodic systems and uncovers length-dependent transport behaviors in nonequilibrium steady states.

## Key findings

- Fractality is reflected in the spatial dependence of observables in steady states.
- Transport dynamics depend on chain length, with Fibonacci chains showing slower transport.
- Fractal nonequilibrium states may be common in driven critical systems with fractal properties.

## Abstract

We investigate the nonequilibrium response of quasiperiodic systems to boundary driving. In particular we focus on the Aubry-Andr\'e-Harper model at its metal-insulator transition and the diagonal Fibonacci model. We find that opening the system at the boundaries provides a transparent and experimentally viable technique to probe its underlying fractality, which is reflected in the fractal spatial dependence of simple observables (such as magnetization) in the nonequilibrium steady state. We also find that the dynamics in the nonequilibrium steady state depends on the length of the chain chosen: generic length chains harbour qualitatively slower transport (different scaling exponent) than Fibonacci length chains, which is in turn slower than in the closed system. We conjecture that such fractal nonequilibrium steady states should arise in generic driven critical systems that have fractal properties.