Quantum strips in higher dimensions

DOI10.7153/oam-2020-14-41zbMath1462.58016arXiv1906.02431OpenAlexW3089725023MaRDI QIDQ3389279

Katerina Zahradova, David Krejčiřík

Publication date: 10 May 2021

Published in: Operators and Matrices (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1906.02431

zbMATH Keywords

ruled surfacesbound statesDirichlet Laplacianeffective Hamiltonianquantum waveguidesHardy inequalitiesrelatively parallel frame

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Geodesics in global differential geometry (53C22) Curves in Euclidean and related spaces (53A04)

Related Items (4)

Existence of discrete eigenvalues for the Dirichlet Laplacian in a two-dimensional twisted strip ⋮ Spectral analysis on ruled surfaces with combined Dirichlet and Neumann boundary conditions ⋮ The asymptotic behaviour of the heat equation in a sheared unbounded strip ⋮ Spectral properties of relativistic quantum waveguides

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Spectral analysis in thin tubes with axial heterogeneities
• The Brownian traveller on manifolds
• Waveguides with asymptotically diverging twisting
• Strong confinement limit for the nonlinear Schrödinger equation constrained on a curve
• The adiabatic limit of Schrödinger operators on fibre bundles
• Ruled strips with asymptotically diverging twisting
• The NLS limit for Bosons in a quantum waveguide
• A Hardy inequality in twisted waveguides
• Influence of bounded states in the Neumann Laplacian in a thin waveguide
• Two-phase eigenvalue problem on thin domains with Neumann boundary condition.
• Quantum strips on surfaces
• Absolute continuity and band gaps of the spectrum of the Dirichlet Laplacian in periodic waveguides
• Eigenvalue and resonance asymptotics in perturbed periodically twisted tubes: twisting versus bending
• Hardy inequalities in strips on ruled surfaces
• Geometrically induced discrete spectrum in curved tubes
• On the spectrum of curved planar waveguides
• Asymptotic behavior of eigenvalues of the Laplacian on a thin domain under the mixed boundary condition
• Mild singular potentials as effective Laplacians in narrow strips
• Dirichlet Laplacian in a thin twisted strip
• THE EFFECTIVE HAMILTONIAN IN CURVED QUANTUM WAVEGUIDES UNDER MILD REGULARITY ASSUMPTIONS
• REDUCTION OF DIMENSION AS A CONSEQUENCE OF NORM‐RESOLVENT CONVERGENCE AND APPLICATIONS
• Location of the essential spectrum in curved quantum layers
• Bound states in curved quantum waveguides
• Twisting versus bending in quantum waveguides
• There is More than One Way to Frame a Curve
• Effective Hamiltonians in surfaces of thin quantum waveguides
• Resonances near thresholds in slightly twisted waveguides
• Spectral estimates for Dirichlet Laplacian on tubes with exploding twisting velocity
• Norm resolvent approximation of thin homogeneous tubes by heterogeneous ones
• Realizing holonomic constraints in classical and quantum mechanics

This page was built for publication: Quantum strips in higher dimensions