Objectif The project is devoted to problems lying in the intersection of such areas as spectral theory of PDE's, noncommutative geometry, semiclassical asymptotics and quantization, operator extension theory, and fractal geometry. The realisation of this project will contribute to the discovery of new relations between these areas and to understanding the mathematical reasons for the surprising behaviour of physical systems in a magnetic field.New approaches in the following fields will be developed :- use of the Krein resolvent formula for the Laplace-Beltrami operator with a vector potential perturbed by a potential with discrete or fractal support;- localized states for Schroedinger-type operators with periodic potentials;- group theoretical magneto-Bloch analysis and operator extension theory for exactly solvable models;- semiclassical methods for description of spectral data of PDE's corresponding to complex Lagrangian subvarieties and complex vector bundles;- noncommutative geometry for algebras with nonlinear commutation relations corresponding to Coulomb-like potentials and the related construction of(Bessel type) coherent states;- quantum averaging and deaveraging procedure.These approaches will be applied to:- obtaining explicit and asymptotic formulas for the spectrum (or parts of the spectrum) and for eigen functions, including formulas for the exponential splitting and gap length of Laplace- Beltrami and Schroedinger operators corresponding to classical integrable systems (such as geodesic flows on 2-sheres and tori, periodic Toda lattice), and to certain partially integrable systems (Hydrogen atom and ion in a homogeneous magnetic field), as well as to homogeneous flows with periodic point perturbation;- finding conditions for band structure, gap-finiteness and for the appearance of the Landau levels in the spectrum of certain higher dimensional Schroedinger-type operators, obtaining there by the "flux-energy" diagram analogous to the "Hofstadter butterfly", calculation of the Chern numbers and Berry phase for these models. Programme(s) IC-INTAS - International Association for the promotion of cooperation with scientists from the independent states of the former Soviet Union (INTAS), 1993- Thème(s) 2 - Mathematics, Telecommunications, Information Technologies OPEN - OPEN Call Appel à propositions Data not available Régime de financement Data not available Coordinateur Bonn University Contribution de l’UE Aucune donnée Adresse Wegelerstrasse 6 53115 Bonn Allemagne Voir sur la carte Coût total Aucune donnée Participants (7) Trier par ordre alphabétique Trier par contribution de l’UE Tout développer Tout réduire Bolognia University Italie Contribution de l’UE Aucune donnée Adresse Piazza di Porta San Donato 5 40126 Bologna Voir sur la carte Coût total Aucune donnée Humbold Universität zu Berlin Allemagne Contribution de l’UE Aucune donnée Adresse Unter den Linden 6 10099 Berlin Voir sur la carte Coût total Aucune donnée International School for Advanced Studies Italie Contribution de l’UE Aucune donnée Adresse Via Beirut 2-4 34100 Trieste Voir sur la carte Coût total Aucune donnée Mordovian State University Russie Contribution de l’UE Aucune donnée Adresse Bolshevistskaya 68 430000 Saransk Voir sur la carte Coût total Aucune donnée Moscow State Technical University Russie Contribution de l’UE Aucune donnée Adresse B. Trehsviat. per. 68 109028 Moscow Voir sur la carte Coût total Aucune donnée National Academy of Sciences of Ukraine Ukraine Contribution de l’UE Aucune donnée Adresse Tereshchenkivska, 3 252601 Kiev Voir sur la carte Coût total Aucune donnée Russian Academy of Sciences Russie Contribution de l’UE Aucune donnée Adresse Prospekt Vernadskogo 101 117526 Moscow Voir sur la carte Coût total Aucune donnée