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Anomalous Non-Hermitian Open-Boundary Spectrum.

Xi-Xi Bao¹, Gang-Feng Guo¹, Lei Tan^2,3

¹School of Sciences and Arts, Suqian University, Suqian 223800, China.

Entropy (Basel, Switzerland)

|October 25, 2024

Summary

This summary is machine-generated.

Continuum bands are not easily captured by open-boundary spectra as systems grow. Complex eigenvalue counts may decrease in larger non-Hermitian systems, challenging assumptions about system size and ideal scenarios.

Keywords:

continuum bands non-Hermitian skin modes

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Area of Science:

Quantum mechanics
Condensed matter physics
Non-Hermitian systems

Background:

Traditionally, continuum bands were assumed to be easily incorporated into open-boundary spectra.
This assumption held regardless of system size, simplifying theoretical models.

Purpose of the Study:

To investigate the relationship between system size and the behavior of continuum bands and complex eigenvalues under open-boundary conditions.
To challenge the conventional understanding of how system expansion affects spectral properties in non-Hermitian systems.

Main Methods:

Analysis of complex eigenvalues in expanding systems under open-boundary conditions.
Comparison of spectral properties with theoretical predictions for infinite systems.

Main Results:

Complex eigenvalues proliferate slowly and oscillate as system size increases.
Overlap between continuum bands and open-boundary eigenvalues becomes less likely in larger systems.
The number of complex eigenvalues can decrease with increasing system size, contrary to expectations.

Conclusions:

Enlarging system size does not necessarily lead to an infinite-sized system scenario.
Eigenstates in non-Hermitian systems can exhibit Bloch wave-like distributions.
Findings have implications for theoretical and experimental studies of non-Hermitian physics.