American Institute of Mathematical Sciences

Advanced
  • Previous Article
    Existence and continuity of strong solutions of partly dissipative reaction diffusion systems
  • PROC Home
  • This Issue
  • Next Article
    Stochastic wave equations with cubic nonlinearity and Q-regular additive noise in $\mathbb{R}^2$
2011, 2011(Special): 1309-1318. doi: 10.3934/proc.2011.2011.1309

Superradiance problem in a 3D annular domain

Indranil SenGupta 1, , Weisheng Jiang 2, , Bo Sun 3, and  Maria Christina Mariani 1,

1. 

Department of Mathematical Sciences, The University of Texas- El Paso, El Paso, Texas 79968-0514, United States, United States
2. 

College of Mathematics and Statistics, Chongqing University, Chongqing 400044, China
3. 

College of Mathematics and Computers, Changsha University of Science and Technology, Changsha, Hu'nan 410076, China

Received  July 2010 Revised  April 2011 Published  October 2011

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: Sturm-Liouville problem, Quantum optics, Spherical harmonics, Dy- namical systems.
Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.
Citation: Indranil SenGupta, Weisheng Jiang, Bo Sun, Maria Christina Mariani. Superradiance problem in a 3D annular domain. Conference Publications, 2011, 2011 (Special) : 1309-1318. doi: 10.3934/proc.2011.2011.1309
[1]

Russell Johnson, Luca Zampogni. On the inverse Sturm-Liouville problem. Discrete and Continuous Dynamical Systems, 2007, 18 (2&3) : 405-428. doi: 10.3934/dcds.2007.18.405
[2]

Chuan-Fu Yang, Natalia Pavlovna Bondarenko. A partial inverse problem for the Sturm-Liouville operator on the lasso-graph. Inverse Problems and Imaging, 2019, 13 (1) : 69-79. doi: 10.3934/ipi.2019004
[3]

Peter Howard, Alim Sukhtayev. The Maslov and Morse indices for Sturm-Liouville systems on the half-line. Discrete and Continuous Dynamical Systems, 2020, 40 (2) : 983-1012. doi: 10.3934/dcds.2020068
[4]

N. A. Chernyavskaya, L. A. Shuster. Spaces admissible for the Sturm-Liouville equation. Communications on Pure and Applied Analysis, 2018, 17 (3) : 1023-1052. doi: 10.3934/cpaa.2018050
[5]

Guglielmo Feltrin. Multiple positive solutions of a sturm-liouville boundary value problem with conflicting nonlinearities. Communications on Pure and Applied Analysis, 2017, 16 (3) : 1083-1102. doi: 10.3934/cpaa.2017052
[6]

Chuan-Fu Yang, Natalia Pavlovna Bondarenko, Xiao-Chuan Xu. An inverse problem for the Sturm-Liouville pencil with arbitrary entire functions in the boundary condition. Inverse Problems and Imaging, 2020, 14 (1) : 153-169. doi: 10.3934/ipi.2019068
[7]

Rashad M. Asharabi, Jürgen Prestin. Computing eigenpairs of two-parameter Sturm-Liouville systems using the bivariate sinc-Gauss formula. Communications on Pure and Applied Analysis, 2020, 19 (8) : 4143-4158. doi: 10.3934/cpaa.2020185
[8]

Elimhan N. Mahmudov. Optimization of fourth order Sturm-Liouville type differential inclusions with initial point constraints. Journal of Industrial and Management Optimization, 2020, 16 (1) : 169-187. doi: 10.3934/jimo.2018145
[9]

Elimhan N. Mahmudov. Optimal control of Sturm-Liouville type evolution differential inclusions with endpoint constraints. Journal of Industrial and Management Optimization, 2020, 16 (5) : 2503-2520. doi: 10.3934/jimo.2019066
[10]

Raziye Mert, Thabet Abdeljawad, Allan Peterson. A Sturm-Liouville approach for continuous and discrete Mittag-Leffler kernel fractional operators. Discrete and Continuous Dynamical Systems - S, 2021, 14 (7) : 2417-2434. doi: 10.3934/dcdss.2020171
[11]

Günter Leugering, Gisèle Mophou, Maryse Moutamal, Mahamadi Warma. Optimal control problems of parabolic fractional Sturm-Liouville equations in a star graph. Mathematical Control and Related Fields, 2022  doi: 10.3934/mcrf.2022015
[12]

Jan Haskovec, Nader Masmoudi, Christian Schmeiser, Mohamed Lazhar Tayeb. The Spherical Harmonics Expansion model coupled to the Poisson equation. Kinetic and Related Models, 2011, 4 (4) : 1063-1079. doi: 10.3934/krm.2011.4.1063
[13]

Mason A. Porter, Richard L. Liboff. The radially vibrating spherical quantum billiard. Conference Publications, 2001, 2001 (Special) : 310-318. doi: 10.3934/proc.2001.2001.310
[14]

Daomin Cao, Ezzat S. Noussair, Shusen Yan. On the profile of solutions for an elliptic problem arising in nonlinear optics. Discrete and Continuous Dynamical Systems, 2004, 11 (2&3) : 649-666. doi: 10.3934/dcds.2004.11.649
[15]

Xiangjin Xu. Sub-harmonics of first order Hamiltonian systems and their asymptotic behaviors. Discrete and Continuous Dynamical Systems - B, 2003, 3 (4) : 643-654. doi: 10.3934/dcdsb.2003.3.643
[16]

Nicolas Augier, Ugo Boscain, Mario Sigalotti. Semi-conical eigenvalue intersections and the ensemble controllability problem for quantum systems. Mathematical Control and Related Fields, 2020, 10 (4) : 877-911. doi: 10.3934/mcrf.2020023
[17]

Marcin Bugdoł, Tadeusz Nadzieja. A nonlocal problem describing spherical system of stars. Discrete and Continuous Dynamical Systems - B, 2014, 19 (8) : 2417-2423. doi: 10.3934/dcdsb.2014.19.2417
[18]

Fabrice Delbary, Kim Knudsen. Numerical nonlinear complex geometrical optics algorithm for the 3D Calderón problem. Inverse Problems and Imaging, 2014, 8 (4) : 991-1012. doi: 10.3934/ipi.2014.8.991
[19]

Sen Zhang, Guo Zhou, Yongquan Zhou, Qifang Luo. Quantum-inspired satin bowerbird algorithm with Bloch spherical search for constrained structural optimization. Journal of Industrial and Management Optimization, 2021, 17 (6) : 3509-3523. doi: 10.3934/jimo.2020130
[20]

Ruikuan Liu, Tian Ma, Shouhong Wang, Jiayan Yang. Thermodynamical potentials of classical and quantum systems. Discrete and Continuous Dynamical Systems - B, 2019, 24 (4) : 1411-1448. doi: 10.3934/dcdsb.2018214

 Impact Factor: 

Tools

Metrics

  • PDF downloads (76)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy