Softcover ISBN:  9781470448417 
Product Code:  CONM/741 
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Electronic ISBN:  9781470453886 
Product Code:  CONM/741.E 
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Book DetailsContemporary MathematicsVolume: 741; 2020; 206 ppMSC: Primary 05; 60; 81; 82; 90;
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 cuttingedge 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, AbdulRahman, Lemm, Lucia, Nachtergaele, and Young consider decorated AKLT models, and Lemm demonstrates a finitesize 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.ReadershipGraduate students and researchers interested in analysis and mathematical physics.

Table of Contents

Articles

Houssam AbdulRahman, Marius Lemm, Angelo Lucia, Bruno Nachtergaele and Amanda Young  A class of twodimensional 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 manybody 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  Finitesize 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


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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 cuttingedge 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, AbdulRahman, Lemm, Lucia, Nachtergaele, and Young consider decorated AKLT models, and Lemm demonstrates a finitesize 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.

Articles

Houssam AbdulRahman, Marius Lemm, Angelo Lucia, Bruno Nachtergaele and Amanda Young  A class of twodimensional 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 manybody 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  Finitesize 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