Boundary Floquet Control of Bulk non-Hermitian Systems

Abstract: Non-Hermitian systems provide a powerful platform for engineering and controlling nonequilibrium phenomena beyond Hermitian settings, with the presence of non-Hermitian skin effect broadening the scope of dynamical control. Here, we develop a general theory of non-Hermitian systems driven exclusively at their boundaries, providing a unified description of the driving-frequency dependence of bulk spectra and dynamics in the thermodynamic limit. Our framework extends non-Bloch band theory to time-periodic systems at arbitrary boundary driving frequencies. Applying it to representative models, we demonstrate boundary-driving-induced parity-time symmetry breaking, with the driving frequency serving as a control knob and the driving amplitude providing an additional handle in finite-size systems. These results establish boundary Floquet driving as a versatile mechanism for controlling bulk properties of non-Hermitian systems and open new routes for dynamical engineering in driven open systems.