Effective Hamiltonians for Thin Dirichlet Tubes with Varying Cross-Section

Abstract

We show how to translate recent results on effective Hamiltonians for quantum systems constrained to a submanifold by a sharply peaked potential to quantum systems on thin Dirichlet tubes. While the structure of the problem and the form of the effective Hamiltonian stays the same, the difficulties in the proofs are different.

6 pages, 1 figure

References in corpus (2)

• Twisting versus bending in quantum waveguides
• Constrained Quantum Systems as an Adiabatic Problem

Cited by in corpus (6)

• Little Magnetic Book
• Generalised Quantum Waveguides
• Magnetic effects in curved quantum waveguides
• Mathematical predominance of Dirichlet condition for the one-dimensional Coulomb potential
• The magnetic Laplacian in shrinking tubular neighbourhoods of hypersurfaces
• The effective Hamiltonian for thin layers with non-Hermitian Robin-type boundary conditions