Filling up complex spectral regions through non-Hermitian disordered chains

Eigenspectra that fill regions in the complex plane have been intriguing to many, inspiring research from random matrix theory esoteric semi-infinite bounded non-Hermitian lattices. In this work, we propose a simple and robust ansatz for constructing models whose eigenspectra up generic prescribed regions. Our approach utilizes specially designed couplings allow co-existence of eigenstates with continuum localization lengths, mathematically emulating effects boundaries. While some these are necessarily long-ranged, they still far more local than what is possible known ensembles. can be feasibly implemented physical platforms such as classical quantum circuits, harbors very high tolerance imperfections due its stochastic nature.