caa a22 4500 445320389 CHVBK 20180317142702.0 cr unu---uuuuu 170323e20110501xx s 000 0 eng 10.1007/s00023-011-0088-1 doi (NATIONALLICENCE)springer-10.1007/s00023-011-0088-1 Aharonov-Bohm Effect in Resonances of Magnetic Schrödinger Operators with Potentials with Supports at Large Separation [Elektronische Daten] [Ivana Alexandrova, Hideo Tamura] Vector potentials are known to have a direct significance to quantum particles moving in the magnetic field. This is called the Aharonov-Bohm effect and is known as one of the most remarkable quantum phenomena. Here we study this quantum effect through the resonance problem. We consider the scattering system consisting of two scalar potentials and one magnetic field with supports at large separation in two dimensions. The system has trajectories oscillating between these supports. We give a sharp lower bound on the resonance widths as the distances between the three supports go to infinity. The bound is described in terms of the backward amplitude for scattering by each of the scalar potentials and by the magnetic field, and it also depends heavily on the magnetic flux of the field. Springer Basel AG, 2011 Alexandrova Ivana Department of Mathematics and Statistics, State University of New York, 1400 Washington Avenue, ES 110, 12222, Albany, NY, USA aut Tamura Hideo Department of Mathematics, Okayama University, 700-8530, Okayama, Japan aut Annales Henri Poincaré SP Birkhäuser Verlag Basel 12/4(2011-05-01), 679-721 1424-0637 12:4<679 2011 12 23 https://doi.org/10.1007/s00023-011-0088-1 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00023-011-0088-1 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Alexandrova Ivana Department of Mathematics and Statistics, State University of New York, 1400 Washington Avenue, ES 110, 12222, Albany, NY, USA aut NATIONALLICENCE 700 1- Tamura Hideo Department of Mathematics, Okayama University, 700-8530, Okayama, Japan aut NATIONALLICENCE 773 0- Annales Henri Poincaré SP Birkhäuser Verlag Basel 12/4(2011-05-01), 679-721 1424-0637 12:4<679 2011 12 23 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer