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2019 The quantum Sabine law for resonances in transmission problems
Jeffrey Galkowski
Pure Appl. Anal. 1(1): 27-100 (2019). DOI: 10.2140/paa.2019.1.27

Abstract

We prove a quantum version of the Sabine law from acoustics describing the location of resonances in transmission problems. This work extends the work of the author 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.

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Jeffrey Galkowski. "The quantum Sabine law for resonances in transmission problems." Pure Appl. Anal. 1 (1) 27 - 100, 2019. https://doi.org/10.2140/paa.2019.1.27

Information

Received: 24 April 2018; Revised: 25 June 2018; Accepted: 8 August 2018; Published: 2019
First available in Project Euclid: 4 February 2019

zbMATH: 07027485
MathSciNet: MR3900029
Digital Object Identifier: 10.2140/paa.2019.1.27

Subjects:
Primary: 35P20, 35P25

Rights: Copyright © 2019 Mathematical Sciences Publishers

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