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Uniform approximation of the integrated density of states for long-range percolation Hamiltonians
the integrated density of states long-range percolation Hamiltonians
2010/11/23
In this paper we study the spectrum of long-range percolation graphs. The underlying geometry is given in terms of a finitely generated amenable group. We prove that the integrated density of states (...
Wigner quantization of some one-dimensional Hamiltonians
Wigner quantization one-dimensional Hamiltonians
2010/11/15
Recently, several papers have been dedicated to the Wigner quantization of different Hamiltonians. In these examples, many interesting mathematical and physical properties have been shown. Among those...
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...
Strong and weak semiclassical limits for some rough Hamiltonians
semiclassical limits rough Hamiltonians
2010/11/12
We present several results concerning the semiclassical limit of the time dependent Schr\"odinger equation with potentials whose regularity doesn't guarantee the uniqueness of the underlying classical...
Integrable Henon-Heiles Hamiltonians: a Poisson algebra approach
Integrable Henon-Heiles Hamiltonians Poisson algebra approach
2010/11/19
The three integrable two-dimensional Henon-Heiles systems and their integrable perturbations are revisited. A family of new integrable perturbations is found, and N-dimensional completely integrable ...