Universal non-Hermitian transport in disordered systems
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914009992658944 |
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| author | Li, Bo Chen, Chuan Wang, Zhong |
| author_facet | Li, Bo Chen, Chuan Wang, Zhong |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_19905 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Universal non-Hermitian transport in disordered systems Li, Bo Chen, Chuan Wang, Zhong Quantum Physics Disordered Systems and Neural Networks Statistical Mechanics Optics 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. |
| title | Universal non-Hermitian transport in disordered systems |
| topic | Quantum Physics Disordered Systems and Neural Networks Statistical Mechanics Optics |
| url | https://arxiv.org/abs/2411.19905 |