Spectra of soft ring graphs

P. Exner; M. Tater

doi:10.1088/0959-7174/14/1/010

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arXiv · math-ph/0303006

Spectra of soft ring graphs

P. Exner·M. Tater

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Abstract

We discuss of a ring-shaped soft quantum wire modeled by $δ$ interaction supported by the ring of a generally nonconstant coupling strength. We derive condition which determines the discrete spectrum of such systems, and analyze the dependence of eigenvalues and eigenfunctions on the coupling and ring geometry. In particular, we illustrate that a random component in the coupling leads to a localization. The discrete spectrum is investigated also in the situation when the ring is placed into a homogeneous magnetic field or threaded by an Aharonov-Bohm flux and the system exhibits persistent currents.

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BibTeX RIS

P. Exner, M. Tater. 2003-03-03. Spectra of soft ring graphs. https://doi.org/10.1088/0959-7174%2F14%2F1%2F010

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