Spectrum of Hatano-Nelson model with strictly ergodic potentials

2023/11/16 by Xueyin Wang, Wang, Xueyin, Zhenfu Wang +5
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Protein Structure and Dynamics #Quantum chaos and dynamical systems #Spectral Theory (math.SP) #stochastic dynamics and bifurcation

paper · pdf · doi:10.48550/arxiv.2311.09899

openalex publication_date 2023/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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 ℓ²(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 \citeDav01A, Dav01, Dav02.

Related

• Spectral transition line for the extended Harper's model in the positive Lyapunov exponent regime
• Dense Phenomena for Ergodic Schrödinger Operators: I. Spectrum, Integrated Density of States, and Lyapunov Exponent
• The Spectrum of Schrödinger Operators with Randomly Perturbed Ergodic Potentials
• Lyapunov exponents in complex dynamics and potential theory
• Full Spectrum of Lyapunov Exponents in Gauge Field Theory