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By means of the operator extension theory, we construct an explicitly solvable model of a simple-cubic three-dimensional regimented array of quantum dots in the presence of a uniform magnetic field. The spectral properties of the model are studied. I
Externí odkaz:
http://arxiv.org/abs/cond-mat/0605629
Publikováno v:
J. Math. Phys. 45 (2004), 1267-1290
The spectral properties of the quantum mechanical system consisting of a quantum dot with a short-range attractive impurity inside the dot are investigated in the zero-range limit. The Green function of the system is obtained in an explicit form. In
Externí odkaz:
http://arxiv.org/abs/math-ph/0310040
A method of building and investigation of the Fermi surfaces for three-dimensional crystals subjected to a uniform magnetic field is presented. The Hamiltonian of a charged particle in the crystal is treated in the framework of the zero-range potenti
Externí odkaz:
http://arxiv.org/abs/cond-mat/0310501
Flux-energy and angle-energy diagrams for an exact three-dimensional Hamiltonian of the Bloch electron in a uniform magnetic field are analyzed. The dependence of the structure of the diagrams on the direction of the field, the geometry of the Bravai
Externí odkaz:
http://arxiv.org/abs/cond-mat/0306391
Publikováno v:
J. Phys. A36 (2003), 4875-4890
We study a free quantum motion on periodically structured manifolds composed of elementary two-dimensional "cells" connected either by linear segments or through points where the two cells touch. The general theory is illustrated with numerous exampl
Externí odkaz:
http://arxiv.org/abs/math-ph/0212052
Autor:
Bruening, J., Geyler, V.
The quantum-mechanical scattering on a compact Riemannian manifold with semi-axes attached to it (hedgehog-shaped manifold) is considered. The complete description of the spectral structure of Schroedinger operators on such a manifold is done, the pr
Externí odkaz:
http://arxiv.org/abs/math-ph/0205030
We have proposed a semiclassical explanation of the geometric structure of the spectrum for the two-dimensional Landau Hamiltonian with a two-periodic electric field without any additional assumptions on the potential. Applying an iterative averaging
Externí odkaz:
http://arxiv.org/abs/cond-mat/0205443
The problem of averaging for systems with one fast phase was considered from various points of view in many papers. The averaging method of Krylov and Bogolyubov and methods of KAM theory originated this line of research, the most complete results we
Externí odkaz:
http://arxiv.org/abs/math/0105164
Publikováno v:
In Procedia CIRP 2017 66:74-78
