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Superradiance problem in a 3D annular domain

Pages: 1309 - 1318, Issue Special, September 2011

 Abstract        Full Text (370.9K)              

Indranil SenGupta - Department of Mathematical Sciences, The University of Texas- El Paso, El Paso, Texas 79968-0514, United States (email)
Weisheng Jiang - College of Mathematics and Statistics, Chongqing University, Chongqing 400044, China (email)
Bo Sun - College of Mathematics and Computers, Changsha University of Science and Technology, Changsha, Hu'nan 410076, China (email)
Maria Christina Mariani - Department of Mathematical Sciences, The University of Texas- El Paso, El Paso, Texas 79968-0514, United States (email)

Abstract: Superradiance is an important phenomena in quantum mechanics which has many practical applications. Recently the superradiance integral equation in three-dimensional balls has been extensively studied. In this paper we consider the superradiance integral equation over an annulus. A differential operator that commutes with the radial part of the superradiance integral equation is found. A complete orthogonal basis for the problem is derived. A generalization is given for the problem.

Keywords:  Quantum optics, Spherical harmonics, Sturm-Liouville problem, Dy- namical systems
Mathematics Subject Classification:  Primary: 58F15, 58F17; Secondary: 53C35

Received: July 2010;      Revised: April 2011;      Published: October 2011.