Year: 2025
Type: article
Abstract: The competition between non-Hermitian skin effect and Anderson localization leads to various intriguing phenomena concerning spectrums and wave functions. Here, we study the linear response of disordered non-Hermitian systems, which is precisely described by the Green's function. We show that the average maximum value of matrix elements of Green's functions, which quantifies the maximal response against an external perturbation, exhibits different phases characterized by different scaling behaviors with respect to the system size. Whereas the exponential-growth phase is also seen in the translation-invariant systems, the algebraic-growth phase is unique to disordered non-Hermitian systems. We explain the numerical findings using the large deviation theory, which provides analytical insights into the algebraic scaling factors of non-Hermitian disordered Green's functions. Furthermore, we show that these scaling behaviors can be observed in the steady states of disordered open quantum systems, offering a quantum-mechanical avenue for their experimental detection. Our work highlights an unexpected interplay between non-Hermitian skin effect and Anderson localization.
Authors: Yin-Quan Huang, Yu-Min Hu, Wen-Tan Xue, Zhong Wang
Institutions: Tsinghua University, National University of Singapore
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: G5473310487, G5583762948, G90414126
OpenAlex ID: W4407697373