Quantum lattice transport along an infinitely extended perturbation

Table of Contents

1. Summary
2. Highlights
3. Key Insights
4. Mindmap
5. Citation

Summary

The paper studies the quantum lattice transport along an infinitely extended perturbation, analyzing the band spectrum of a periodic quantum graph with a δ-coupling of strength γ in the vertices perturbed by changing the latter at an infinite straight array of vertices to a γ ̸= γ.

Highlights

• The authors consider a periodic quantum graph in the form of a rectangular lattice with a δ-coupling of strength γ in the vertices.
• The perturbation is introduced by changing the coupling strength to γ ̸= γ at an infinite straight array of vertices.
• The spectrum of the unperturbed system is analyzed using the Floquet-Bloch theory.
• The authors prove that the spectrum remains preserved as a set provided γ ̸= γ > 0.
• For all other combinations, additional bands appear in some or all gaps of the unperturbed system.
• The probability of existence of a state exponentially localized in the vicinity of the perturbation equals 1.
• The high-energy behavior of the spectrum is also analyzed.

Key Insights

• The authors use the Floquet-Bloch theory to analyze the spectrum of the unperturbed system, which is a powerful tool for studying periodic systems.
• The introduction of the perturbation leads to the appearance of new spectral bands, which can be analyzed using the band conditions derived in the paper.
• The authors prove that the spectrum remains preserved as a set provided γ ̸= γ > 0, which is an interesting result that sheds light on the behavior of the system under perturbation.
• The high-energy behavior of the spectrum is also analyzed, and the authors show that the probability of existence of a state exponentially localized in the vicinity of the perturbation equals 1.
• The paper provides a detailed analysis of the band-gap structure of the spectrum, which is an important aspect of quantum systems.
• The authors use a combination of analytical and numerical methods to study the system, which provides a comprehensive understanding of the behavior of the system.
• The results of the paper have implications for the study of quantum transport in periodic systems, which is an active area of research in condensed matter physics.

Mindmap

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Citation

Baradaran, M., Exner, P., & Khrabustovskyi, A. (2024). Quantum lattice transport along an infinitely extended perturbation (Version 1). arXiv. https://doi.org/10.48550/ARXIV.2412.20919