Quantum singular operator limits of thin Dirichlet tubes via \(\Gamma\)-convergence

DOI10.1016/S0034-4877(11)00007-3zbMath1241.81073arXiv1010.2101OpenAlexW3099141528MaRDI QIDQ410673

César R. de Oliveira

Publication date: 3 April 2012

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1010.2101

zbMATH Keywords

\(\Gamma\)-convergencesingular operatorsbroken linequantum thin tubes

Mathematics Subject Classification ID

Asymptotic distributions of eigenvalues in context of PDEs (35P20) Schrödinger operator, Schrödinger equation (35J10) Perturbation theories for operators and differential equations in quantum theory (81Q15) Variational methods for eigenvalues of operators (49R05)

Related Items (10)

THE EFFECTIVE HAMILTONIAN IN CURVED QUANTUM WAVEGUIDES UNDER MILD REGULARITY ASSUMPTIONS ⋮ Influence of bounded states in the Neumann Laplacian in a thin waveguide ⋮ Effective Hamiltonians in surfaces of thin quantum waveguides ⋮ The adiabatic limit of Schrödinger operators on fibre bundles ⋮ Lifshits tails for randomly twisted quantum waveguides ⋮ CONVERGENCE OF SOLUTIONS TO SOME ELLIPTIC EQUATIONS IN BOUNDED NEUMANN THIN DOMAINS ⋮ On Norm Resolvent and Quadratic Form Convergences in Asymptotic Thin Spatial Waveguides ⋮ Mathematical predominance of Dirichlet condition for the one-dimensional Coulomb potential ⋮ Norm resolvent convergence of Dirichlet Laplacian in unbounded thin waveguides ⋮ Thin waveguides with Robin boundary conditions

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