Boundary Floquet Control of Bulk non-Hermitian Systems

TL;DR

This paper demonstrates that boundary-driven Floquet perturbations can control bulk properties in non-Hermitian systems exhibiting the skin effect, through a developed non-Bloch band theory.

Contribution

It introduces a Floquet non-Bloch band theory for boundary-driven non-Hermitian systems, enabling bulk property manipulation via boundary driving.

Findings

Boundary Floquet driving reconstructs bulk spectra and dynamics.

Boundary driving frequency influences non-Bloch PT symmetry breaking.

Amplitude of boundary driving acts as a finite-size control parameter.

Abstract

Boundary perturbations are generally irrelevant for bulk properties in the thermodynamic limit, as they are edge-confined and subextensive. We show that this expectation breaks down in boundary-driven systems exhibiting the non-Hermitian skin effect, where arbitrarily weak boundary Floquet driving reconstructs bulk quasienergy spectra and dynamics. We develop a Floquet non-Bloch band theory that extends generalized Brillouin-zone methods to boundary-driven systems at arbitrary driving frequencies, overcoming the lack of a general framework beyond high-frequency approximations. With representative single- and two-band models, we demonstrate that the boundary driving frequency tunes non-Bloch parity-time symmetry breaking, while its amplitude acts as a finite-size control parameter. Our work establishes boundary Floquet control as a general route for manipulating bulk properties, opening a new avenue for dynamical engineering in driven open systems.