Galkowski, J;
(2019)
The Quantum Sabine Law for Resonances in Transmission Problems.
Pure and Applied Analysis
, 1
(1)
pp. 27-100.
10.2140/paa.2019.1.27.
Preview |
Text
Galkowski_paa-v1-n1-p02-p.pdf - Published Version Download (3MB) | Preview |
Abstract
We prove a quantum version of the Sabine law from acoustics describing the location of resonances in transmission problems. This work extends the author's previous work to a broader class of systems. Our main applications are to scattering by transparent obstacles, scattering by highly frequency dependent delta potentials, and boundary stabilized wave equations. We give a sharp characterization of the resonance free regions in terms of dynamical quantities. In particular, we relate the imaginary part of resonances or generalized eigenvalues to the chord lengths and reflectivity coefficients for the ray dynamics, thus proving a quantum version of the Sabine law.
| Type: | Article |
|---|---|
| Title: | The Quantum Sabine Law for Resonances in Transmission Problems |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.2140/paa.2019.1.27 |
| Publisher version: | http://dx.doi.org/10.2140/paa.2019.1.27 |
| Language: | English |
| Additional information: | First published in Pure and Applied Analysis in Vol. 1 (2019), No. 1, published by Mathematical Sciences Publishers. |
| Keywords: | transmission, resonances, boundary integral operators, transparent, scattering. |
| 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-pp.ucl.ac.uk/id/eprint/10083898 |
Archive Staff Only
 |
View Item |
