Soft quantum waveguides in three dimensions

Abstract

We discuss a three-dimensional soft quantum waveguide, in other words, Schrödinger operator in ${\mathbb{R}}^3$ with an attractive potential supported by an infinite tube and keeping its transverse profile fixed. We show that if the tube is asymptotically straight, the distance between its ends is unbounded, and its twist satisfies the so-called Tang condition, the esential spectrum is not affected by smooth bends. Furthermore, we derive a sufficient condition, expressed in terms of the tube geometry, for the discrete spectrum of such an operator to be nonempty.

Minor improvement, a few references added; to appear in J. Math. Phys

References in corpus (4)

• Bound states due to a strong $\delta$ interaction supported by a curved surface
• Spectral properties of soft quantum waveguides
• Soft quantum waveguides with an explicit cut-locus
• Optimization of the lowest eigenvalue of a soft quantum ring

Cited by in corpus (2)

• 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