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9781470485351 Academic Inspection Copy

Mathematical Theories for Metamaterials

From Condensed Matter Theory to Subwavelength Physics
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This book develops a rigorous mathematical theory of subwavelength physics derived from first principles, providing a unified framework for the analysis of phenomena arising in metamaterials. It demonstrates the challenges, excitement, and opportunities for research at the interface of mathematics and wave physics. Based on the 2024 NSF-CBMS conference Mathematical Methods for Novel Metamaterials, held at Auburn University, the volume expands on the first author's CBMS lecture series on the mathematical foundations of subwavelength physics. It is written for graduate students and researchers in mathematics interested in condensed matter theory, wave physics, metamaterials, topological materials, and scattering resonances. The exposition is self-contained and assumes only a standard background in partial differential equations.
Habib Ammari, ETH Zurich, Switzerland, Bryn Davies, University of Warwick, Coventry, United Kingdom, and Erik Orvehed Hiltunen, University of Oslo, Norway
Part 1. Finite systems of subwavelength resonators; Subwavelength resonances; Exceptional points in non-Hermitian systems of subwavelength resonators; Effective medium theory for finite systems of weakly interacting subwavelength resonators; Part 2. Periodic systems of subwavelength resonators; Hermitian systems of subwavelength resonators; Non-Hermitian systems of subwavelength resonators; Part 3. Convergence results for large finite systems of subwavelength resonators; Spectral convergence of defect modes; Convergence to the essential spectrum and band structure; Concluding remarks and open problems; Appendix A. Some basic results; Appendix B. Layer potential techniques; Appendix C. Some technical results and proofs; Bibliography; Index
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