Non-Hermitian Spectral Topology Shaped by Memory
Abstract
Non-Hermitian spectral topology has transformed our understanding of bulk--boundary correspondence in open systems, yet its exploration has largely remained within the Markovian regime of instantaneous coupling. Here, we reveal how memory shapes non-Hermitian spectral topology by extending coupling asymmetry from space to time. Spatiotemporal nonreciprocity and memory-induced spectral multivaluedness give rise to nontrivial spectral topology on multi-sheeted Riemann surfaces, governed by both spatial connectivity and interaction history. Coherent interference among long-range memory channels can induce anomalous spectral winding and skin localization opposite to the dominant-coupling direction. Moreover, asymmetric retardation alone can generate non-Hermitian spectral topology and skin accumulation even in the absence of spatial coupling asymmetry. Channel dissipation further drives topological transitions that reverse the skin effect, with a critical point at matched channel and lattice decay rates. We validate the anomalous skin effect and its dissipation-controlled reversal through full-wave simulations and microwave experiments. Our results establish time nonlocality as a fundamental degree of freedom in non-Hermitian topology, revealing phenomena inaccessible within the Markovian paradigm.
Related
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BibTeX
@misc{pan2026nonhermitian,
title = {{Non-Hermitian Spectral Topology Shaped by Memory}},
author = {Hao Pan and Bo Xue and Wanyue Xiao and Qiuyang Li and Yuqiong Cheng and Yumeng Wang and Kun Ding and Alex M. H. Wong and Shubo Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.41370},
eprint = {2610.41370},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.41370},
}
RIS
TY - UNPB
TI - Non-Hermitian Spectral Topology Shaped by Memory
AU - Hao Pan
AU - Bo Xue
AU - Wanyue Xiao
AU - Qiuyang Li
AU - Yuqiong Cheng
AU - Yumeng Wang
AU - Kun Ding
AU - Alex M. H. Wong
AU - Shubo Wang
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.41370
UR - https://arxiv.org/abs/2610.41370
AB - Non-Hermitian spectral topology has transformed our understanding of bulk--boundary correspondence in open systems, yet its exploration has largely remained within the Markovian regime of instantaneous coupling. Here, we reveal how memory shapes non-Hermitian spectral topology by extending coupling asymmetry from space to time. Spatiotemporal nonreciprocity and memory-induced spectral multivaluedness give rise to nontrivial spectral topology on multi-sheeted Riemann surfaces, governed by both spatial connectivity and interaction history. Coherent interference among long-range memory channels can induce anomalous spectral winding and skin localization opposite to the dominant-coupling direction. Moreover, asymmetric retardation alone can generate non-Hermitian spectral topology and skin accumulation even in the absence of spatial coupling asymmetry. Channel dissipation further drives topological transitions that reverse the skin effect, with a critical point at matched channel and lattice decay rates. We validate the anomalous skin effect and its dissipation-controlled reversal through full-wave simulations and microwave experiments. Our results establish time nonlocality as a fundamental degree of freedom in non-Hermitian topology, revealing phenomena inaccessible within the Markovian paradigm.
ER -