Mathematical Challenges of Zero-Range Physics
Models, Methods, Rigorous Results, Open Problems
Editors: Michelangeli, Alessandro (Ed.)
Free Preview- Original results closing relevant problems in the community
- Pedagogical presentation of key technical tools
- Transversal language by applied mathematicians and theoretical physicists
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- About this book
-
Since long over the decades there has been a large transversal community of mathematicians grappling with the sophisticated challenges of the rigorous modelling and the spectral and scattering analysis of quantum systems of particles subject to an interaction so much localised to be considered with zero range. Such a community is experiencing fruitful and inspiring exchanges with experimental and theoretical physicists. This volume reflects such spirit, with a diverse range of original contributions by experts, presenting an up-to-date collection of most relevant results and challenging open problems. It has been conceived with the deliberate two-fold purpose of serving as an updated reference for recent results, mathematical tools, and the vast related literature on the one hand, and as a bridge towards several key open problems that will surely form the forthcoming research agenda in this field.
- About the authors
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Alessandro Michelangeli is at present a von Humboldt Experienced Researcher at the Institute of Applied Mathematics and at the Hausdorff Center for Mathematics at the university of Bonn. His research is at the interface of mathematical physics, functional analysis, partial differential equations, and operator theory, with a special focus on problems and methods for quantum mechanics. He graduated in theoretical physics in Pisa and in mathematical physics at SISSA Trieste, held faculty positions at the LMU Munich and SISSA Trieste, and visiting positions at the University of Cambridge, SISSA Trieste, and Bilkent.
- Table of contents (13 chapters)
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Thermodynamic Properties of Ultracold Fermi Gases Across the BCS-BEC Crossover and the Bertsch Problem
Pages 1-33
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Scattering Theory for Delta-Potentials Supported by Locally Deformed Planes
Pages 35-55
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The Massless Nelson Hamiltonian and Its Domain
Pages 57-80
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A Note on the Dirac Operator with Kirchoff-Type Vertex Conditions on Metric Graphs
Pages 81-104
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Dirac Operators and Shell Interactions: A Survey
Pages 105-131
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Table of contents (13 chapters)
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Bibliographic Information
- Bibliographic Information
-
- Book Title
- Mathematical Challenges of Zero-Range Physics
- Book Subtitle
- Models, Methods, Rigorous Results, Open Problems
- Editors
-
- Alessandro Michelangeli
- Series Title
- Springer INdAM Series
- Series Volume
- 42
- Copyright
- 2021
- Publisher
- Springer International Publishing
- Copyright Holder
- The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG
- eBook ISBN
- 978-3-030-60453-0
- DOI
- 10.1007/978-3-030-60453-0
- Hardcover ISBN
- 978-3-030-60452-3
- Series ISSN
- 2281-518X
- Edition Number
- 1
- Number of Pages
- VIII, 329
- Number of Illustrations
- 7 b/w illustrations, 9 illustrations in colour
- Topics
