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Effective Hamiltonians for Thin Dirichlet Tubes with Varying Cross-Section
Effective Hamiltonians Thin Dirichlet Tubes Cross-Section
2010/11/22
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 s...
Quantum singular operator limits of thin Dirichlet tubes via $\Gamma$-convergence
Quantum singular operator limits thin Dirichlet tubes $\Gamma$-convergence
2010/11/11
The $\Gamma$-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 Di...