Scattering of particles bounded to an infinite planar curve

Abstract

Non-relativistic quantum particles bounded to a curve in R^2 by attractive contact $\delta$-interaction are considered. The interval between the energy of the transversal bound state and zero is shown to belong to the absolutely continuous spectrum, with possible embedded eigenvalues. The existence of the wave operators is proved for the mentioned energy interval using the Hamiltonians with the interaction supported by the straight lines as the free ones. Their completeness is not proved. The curve is assumed C^3-smooth, non-intersecting, unbounded, asymptotically approaching two different half-lines (non-parallel or parallel but excluding the "U-case"). Physically, the system can be considered as a model of long nanostructural channel.

43 pages

References in corpus (5)

• Spectra of self-adjoint extensions and applications to solvable Schroedinger operators
• Schrödinger operators with delta and delta'-potentials supported on hypersurfaces
• Limiting Absorption Principle, Generalized Eigenfunctions and Scattering Matrix for Laplace Operators with Boundary conditions on Hypersurfaces
• Spectral enclosures for non-self-adjoint extensions of symmetric operators
• Asymptotic Completeness and S-Matrix for Singular Perturbations

Cited by in corpus (1)

• Spectral properties of soft quantum waveguides