A geometric Iwatsuka type effect in quantum layers.

@article{Exner2017AGI,
  title={A geometric Iwatsuka type effect in quantum layers.},
  author={Pavel Exner and T. Kalvoda and Matvej Tuvsek},
  journal={arXiv: Mathematical Physics},
  year={2017}
}
We study motion of a charged particle confined to Dirichlet layer of a fixed width placed into a homogeneous magnetic field. If the layer is planar and the field is perpendicular to it the spectrum consists of infinitely degenerate eigenvalues. We consider translationally invariant geometric perturbations and derive several sufficient conditions under which a magnetic transport is possible, that is, the spectrum, in its entirety or a part of it, becomes absolutely continuous. 
[PDF] Semantic Reader
3 Citations

Figures from this paper

3 Citations

Magnetic transport in laterally coupled layers

We discuss magnetic transport in the system of two adjacent hard-wall layers exposed to a homogeneous field perpendicular to the layer plane and coupled laterally through a strip-shaped window in the…

Absence of embedded eigenvalues for translationally invariant magnetic Laplacians

Translationnally invariant bidimensional magnetic Laplacians are considered. Using an improved version of the harmonic approximation, we establish the absence of point spectrum under various…

A Complete Bibliography of Publications in the Journal of Mathematical Physics: 2005{2009

(2 < p < 4) [200]. (Uq(∫u(1, 1)), oq1/2(2n)) [92]. 1 [273, 79, 304, 119]. 1 + 1 [252]. 2 [352, 318, 226, 40, 233, 157, 299, 60]. 2× 2 [185]. 3 [456, 363, 58, 18, 351]. ∗ [238]. 2 [277]. 3 [350]. p…

References

SHOWING 1-10 OF 25 REFERENCES

On an extension of the Iwatsuka model

We prove absolute continuity for an extended class of two-dimensional magnetic Hamiltonians that were initially studied by Iwatsuka. In particular, we add an electric field that is translation…

Magnetic strip waveguides

We analyse the spectrum of the `local' Iwatsuka model, i.e. a two-dimensional charged particle interacting with a magnetic field which is homogeneous outside a finite strip and translationally…

Some Propagation Properties of the Iwatsuka Model

Abstract:In this paper we study a two dimensional magnetic field Schrödinger Hamiltonian introduced in [7]. This model has some interesting propagation properties, as conjectured in [2] and at the…

The Magnetic Laplacian in Shrinking Tubular Neighborhoods of Hypersurfaces

The Dirichlet Laplacian between two parallel hypersurfaces in Euclidean spaces of any dimension in the presence of a magnetic field is considered in the limit when the distance between the…

Edge Currents for Quantum Hall Systems, II. Two-Edge, Bounded and Unbounded Geometries

Abstract.Devices exhibiting the integer quantum Hall effect can be modeled by one-particle Schrödinger operators describing the planar motion of an electron in a perpendicular, constant magnetic…

Quantization of Edge Currents along Magnetic Barriers and Magnetic Guides

We investigate the edge conductance of particles submitted to an Iwatsuka magnetic field, playing the role of a purely magnetic barrier. We also consider magnetic guides generated by generalized…

The constrained quantum mechanical harmonic oscillator

  • P. Dean
  • Physics
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 1966
Abstract The effect of restricting the displacements of a quantum mechanical harmonic oscillator to semi-infinite and finite regions is studied. It is shown how the eigenvalue problem may be solved,…

Structure of the spectrum of the Schrodinger operator with magnetic field in a?strip and infinite-gap potentials

The Sturm-Liouville operator on an?interval with zero boundary conditions is considered; here is a?strictly convex function of class on the real line and is a?numerical parameter. The?dependence of…

Schrodinger Operators: With Application to Quantum Mechanics and Global Geometry

Self-Adjointness.- Lp-Properties of Eigenfunctions, and All That.- Geometric Methods for Bound States.- Local Commutator Estimates.- Phase Space Analysis of Scattering.- Magnetic Fields.- Electric…

Edge currents and eigenvalue estimates for magnetic barrier Schrödinger operators

It is proved that the eigenvalues of an Airy operator, respectively, harmonic oscillator operator, describe the asymptotic behavior of the band functions for large negative, respectively positive, wave numbers and the existence of absolutely continuous spectrum in certain energy intervals is established.