Universal non-Hermitian transport in disordered systems

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.

7+10 pages,3+3 figures

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Cited by in corpus (5)

• Non-Hermitian Second-Order Topological Phases and Bipolar Skin Effect in Photonic Kagome Crystals
• Lifshitz tail states in non-Hermitian disordered photonic lattices
• Solution of Wave Acceleration and Non-Hermitian Jump in Nonreciprocal Lattices
• Dynamics and steady states of tight-binding chains in presence of isolated defects
• Asymptotically exact solution of the non-Hermitian disordered interacting Hatano-Nelson chain