Cel 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. Program(-y) IC-INTAS - International Association for the promotion of cooperation with scientists from the independent states of the former Soviet Union (INTAS), 1993- Temat(-y) 2 - Mathematics, Telecommunications, Information Technologies OPEN - OPEN Call Zaproszenie do składania wniosków Data not available System finansowania Data not available Koordynator Bonn University Wkład UE Brak danych Adres Wegelerstrasse 6 53115 Bonn Niemcy Zobacz na mapie Koszt całkowity Brak danych Uczestnicy (7) Sortuj alfabetycznie Sortuj według wkładu UE Rozwiń wszystko Zwiń wszystko Bolognia University Włochy Wkład UE Brak danych Adres Piazza di Porta San Donato 5 40126 Bologna Zobacz na mapie Koszt całkowity Brak danych Humbold Universität zu Berlin Niemcy Wkład UE Brak danych Adres Unter den Linden 6 10099 Berlin Zobacz na mapie Koszt całkowity Brak danych International School for Advanced Studies Włochy Wkład UE Brak danych Adres Via Beirut 2-4 34100 Trieste Zobacz na mapie Koszt całkowity Brak danych Mordovian State University Rosja Wkład UE Brak danych Adres Bolshevistskaya 68 430000 Saransk Zobacz na mapie Koszt całkowity Brak danych Moscow State Technical University Rosja Wkład UE Brak danych Adres B. Trehsviat. per. 68 109028 Moscow Zobacz na mapie Koszt całkowity Brak danych National Academy of Sciences of Ukraine Ukraina Wkład UE Brak danych Adres Tereshchenkivska, 3 252601 Kiev Zobacz na mapie Koszt całkowity Brak danych Russian Academy of Sciences Rosja Wkład UE Brak danych Adres Prospekt Vernadskogo 101 117526 Moscow Zobacz na mapie Koszt całkowity Brak danych