Quantum lattice transport along an infinitely extended perturbation

Marzieh Baradaran; Pavel Exner; Andrii Khrabustovskyi

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arXiv · 2412.20919

Quantum lattice transport along an infinitely extended perturbation

Marzieh Baradaran·Pavel Exner·Andrii Khrabustovskyi

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Abstract

We consider a periodic quantum graph in the form of a rectangular lattice with the $\delta$-coupling of strength $\gamma$ in the vertices perturbed by changing the latter at an infinite straight array of vertices to a $\widetilde\gamma\ne\gamma$. We analyze the band spectrum of the system and show that it remains preserved as a set provided $\widetilde\gamma>\gamma>0$ while for all the other combinations additional band appear in some or all gaps of the unperturbed system. We also prove that for a randomly chosen positive energy, the probability of existence of a state exponentially localized in the vicinity of the perturbation equals $\frac12$.

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BibTeX RIS

Marzieh Baradaran, Pavel Exner, Andrii Khrabustovskyi. 2024-12-30. Quantum lattice transport along an infinitely extended perturbation. https://arxiv.org/abs/2412.20919

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