Analytic Trends in Mathematical Physics
About this Title
Houssam Abdul-Rahman, University of Arizona, Tucson, AZ, Robert Sims, University of Arizona, Tucson, AZ and Amanda Young, University of Arizona, Tucson, AZ, Editors
Publication: Contemporary Mathematics
Publication Year: 2020; Volume 741
ISBNs: 978-1-4704-4841-7 (print); 978-1-4704-5388-6 (online)
This volume contains the proceedings of the Arizona School of Analysis and Mathematical Physics, held from March 5–9, 2018, at the University of Arizona, Tucson, Arizona.
A main goal of this school was to introduce graduate students and postdocs to exciting topics of current research that are both influenced by physical intuition and require the use of cutting-edge mathematics.
The articles in this volume reflect recent progress and innovative techniques developed within mathematical physics. Two works investigate spectral gaps of quantum spin systems. Specifically, Abdul-Rahman, Lemm, Lucia, Nachtergaele, and Young consider decorated AKLT models, and Lemm demonstrates a finite-size criterion for $D$-dimensional models. Bachmann, De Roeck, and Fraas summarize a recent proof of the adiabatic theorem, while Bachmann, Bols, De Roeck, and Fraas discuss linear response for interacting Hall insulators. Models on general graphs are the topic of the articles by Fischbacher, on higher spin XXZ, and by Latushkin and Sukhtaiev, on an index theorem for Schrödinger operators. Probabilistic applications are the focus of the articles by DeMuse and Yin, on exponential random graphs, by Saenz, on KPZ universality, and by Stolz, on disordered quantum spin chains.
In all, the diversity represented here is a testament to the enthusiasm this rich field of mathematical physics generates.
Graduate students and researchers interested in analysis and mathematical physics.
Table of Contents
- Houssam Abdul-Rahman, Marius Lemm, Angelo Lucia, Bruno Nachtergaele and Amanda Young – A class of two-dimensional AKLT models with a gap
- Sven Bachmann, Alex Bols, Wojciech De Roeck and Martin Fraas – Note on linear response for interacting Hall insulators
- Sven Bachmann, Wojciech De Roeck and Martin Fraas – The adiabatic theorem in a quantum many-body setting
- Ryan DeMuse and Mei Yin – Perspectives on exponential random graphs
- Christoph Fischbacher – A Schrödinger operator approach to higher spin XXZ systems on general graphs
- Yuri Latushkin and Selim Sukhtaiev – An index theorem for Schrödinger operators on metric graphs
- Marius Lemm – Finite-size criteria for spectral gaps in $D$-dimensional quantum spin systems
- Axel Saenz – The KPZ universality class and related topics
- Günter Stolz – Aspects of the mathematical theory of disordered quantum spin chains