Galkowski, J;
(2016)
Resonances for thin barriers on the circle.
Journal of Physics A: Mathematical and Theoretical
, 49
(12)
, Article 125205. 10.1088/1751-8113/49/12/125205.
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Abstract
We study high energy resonances for the operator-ΔV, ∂ω :=- Δ +ΔV, ∂ω ⊗ V when V has strong frequency dependence. The operator -ΔV, ∂ω is a Hamiltonian used to model both quantum corrals (Aligia and Lobos 2005 J. Phys.: Condens. Matter 17 S1095, Barr 2010 Nano Lett. 10 325360) and leaky quantum graphs (Exner P 2008 Analysis on Graphs and its Applications (Providence, RI: American Mathematical Society) pp 523564). Since highly frequency dependent delta potentials are out of reach of the more general techniques in (Galkowski J 2015 arXiv:1511.05894, Galkowski J and Smith H 2014 Int. Math. Res. Not.) we study the special case where ω = B(0, 1) CR2 and V =h-αV0 > 0 with α1. Here h-1 ∼ Re∇is the frequency. We give sharp bounds on the size of resonance free regions for α≤ 1 and the location of bands of resonances when 5/6≤α≤ 1. Finally, we give a lower bound on the number of resonances in logarithmic size strips: -MlogRe∇≤Im∇≤0.
Type: | Article |
---|---|
Title: | Resonances for thin barriers on the circle |
Open access status: | An open access version is available from UCL Discovery |
DOI: | 10.1088/1751-8113/49/12/125205 |
Publisher version: | https://doi.org/10.1088/1751-8113/49/12/125205 |
Language: | English |
Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
Keywords: | resonances, quantum corral, delta potential, high energy, leaky quantum graph |
UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
URI: | https://discovery.ucl.ac.uk/id/eprint/10083911 |
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