Spectrum of Hatano-Nelson model with strictly ergodic potentials

Xueyin Wang; Zhenfu Wang; Jiangong You; Qi Zhou

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arXiv · 2311.09899

Spectrum of Hatano-Nelson model with strictly ergodic potentials

Xueyin Wang·Zhenfu Wang·Jiangong You·Qi Zhou

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Abstract

We provide a precise formula for the spectrum of the Hatano-Nelson model with strictly ergodic potentials in terms of its Lyapunov exponent. As applications, one clearly observes the real-complex spectrum transition. Moreover, if the Lyapunov exponent is continuous, the spectrum of the Hatano-Nelson model in $\ell^{2}(\mathbb{Z})$ can be approximated by the spectrum of its finite-interval truncation with periodic boundary conditions. Both of these results are strikingly different from the Hatano-Nelson model with random potentials \cite{Dav01A, Dav01, Dav02}.

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BibTeX RIS

Xueyin Wang, Zhenfu Wang, Jiangong You, Qi Zhou. 2023-11-16. Spectrum of Hatano-Nelson model with strictly ergodic potentials. https://arxiv.org/abs/2311.09899

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