Quantum singular operator limits of thin Dirichlet tubes via $\Gamma$-convergence
Mathematical Physics
2015-05-20 v1 Functional Analysis
math.MP
Quantum Physics
Abstract
The -convergence of lower bounded quadratic forms is used to study the singular operator limit of thin tubes (i.e., the vanishing of the cross section diameter) of the Laplace operator with Dirichlet boundary conditions; a procedure to obtain the effective Schr\"odinger operator (in different subspaces) is proposed, generalizing recent results in case of compact tubes. Finally, after scaling curvature and torsion the limit of a broken line is briefly investigated.
Cite
@article{arxiv.1010.2101,
title = {Quantum singular operator limits of thin Dirichlet tubes via $\Gamma$-convergence},
author = {Cesar R. de Oliveira},
journal= {arXiv preprint arXiv:1010.2101},
year = {2015}
}
Comments
28 pages; no figures; to appear in Rep. Math. Phys