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<p>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 ℓ <sup>2</sup>(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 [11, 12, 13].</p>

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Spectrum of Hatano–Nelson model with strictly ergodic potentials

  • 期刊论文

  • 发表日期：

    2025年10月27日

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  • Xueyin Wang,
  • Zhenfu Wang,
  • Jiangong You,
  • Qi Zhou

摘要

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 ℓ 2(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 [11, 12, 13].