Universal non-Hermitian transport in disordered systems

Bo Li; Chuan Chen; Zhong Wang

doi:10.1103/z9m1-3mwb

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arXiv · 2411.19905

Universal non-Hermitian transport in disordered systems

Bo Li·Chuan Chen·Zhong Wang

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Abstract

In disordered Hermitian systems, localization of energy eigenstates prohibits wave propagation. In non-Hermitian systems, however, wave propagation is possible even when the eigenstates of Hamiltonian are exponentially localized by disorders. We find in this regime that non-Hermitian wave propagation exhibits novel universal scaling behaviors without Hermitian counterpart. Furthermore, our theory demonstrates how the tail of imaginary-part density of states dictates wave propagation in the long-time limit. Specifically, for the three typical classes, namely the Gaussian, the uniform, and the linear imaginary-part density of states, we obtain logarithmically suppressed sub-ballistic transport, and two types of subdiffusion with exponents that depend only on spatial dimensions, respectively. Our work highlights the fundamental differences between Hermitian and non-Hermitian Anderson localization, and uncovers unique universality in non-Hermitian wave propagation.

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quant-ph cond-mat.dis-nn cond-mat.stat-mech physics.optics

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Bo Li, Chuan Chen, Zhong Wang. 2024-11-29. Universal non-Hermitian transport in disordered systems. https://doi.org/10.1103/z9m1-3mwb

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