Analytic Trends in Mathematical Physics

ISBN-13: 9781470448417

Houssam Abdul-Rahman;Robert Sims;Amanda Young

Opis

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 Schrodinger 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.

Spis treści

• H. Abdul-Rahman, M. Lemm, A. Lucia, B. Nachtergaele, and A. Young, A class of two-dimensional AKLT models with a gap
• S. Bachmann, A. Bols, W. De Roeck, and M. Fraas, Note on linear response for interacting Hall insulators
• S. Bachmann, W. De Roeck, and M. Fraas, The adiabatic theoerm in a quantum many-body setting
• R. DeMuse and M. Yin, Perspectives on exponential random graphs
• C. Fischbacher, A Schrodinger operator approach to higher spin XXZ systems on general graphs
• Y. Latushkin and S. Sukhtaiev, An index theorem for Schrodinger operators on metric graphs
• M. Lemm, Finite-size criteria for spectral gaps in $D$-dimensional quantum spin systems
• A. Saenz, The KPZ universality class and related topics
• G. Stolz, Aspects of the mathematical theory of disordered quantum spin chains.