Spectra of soft ring graphs

Details Spectra of soft ring graphs Spectra of soft ring graphs

2003-03-03

arxiv.org/abs/math-ph/0303006v1

Waves in Random Media 14 (2004), S47-60

Physics

Mathematical Physics

LaTeX 2e, 17 pages, with 10 ps figures

Scientific paper

10.1088/0959-7174/14/1/010

We discuss of a ring-shaped soft quantum wire modeled by $\delta$ 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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