Spectral properties of soft quantum waveguides

Abstract

We consider a soft quantum waveguide described by a two-dimensional Schrödinger operators with an attractive potential in the form of a channel of a fixed profile built along an infinite smooth curve which is not straight but it is asymptotically straight in a suitable sense. Using Birman-Schwinger principle we show that the discrete spectrum of such an operator is nonempty if the potential well defining the channel profile is deep and narrow enough. Some related problems are also mentioned.

a few misprints and one minor inconsistency corrected

References in corpus (2)

• Schrödinger operators with $\delta$-interactions supported on conical surfaces
• Edge Currents for Quantum Hall Systems, II. Two-Edge, Bounded and Unbounded Geometries

Cited by in corpus (6)

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• Soft quantum waveguides in three dimensions
• Optimization of the lowest eigenvalue of a soft quantum ring
• Robustness of flat bands on the perturbed Kagome and the perturbed Super-Kagome lattice
• Fermi's golden rule in tunneling models with quantum waveguides perturbed by Kato class measures
• Scattering for Schrödinger operators with conical decay