Analytic trends in mathematical physics / Houssam Abdul-Rahman, Robert Sims, Amanda Young, editors.

Format:

Book

Conference/Event

Author/Creator:

Abdul Rahman, Houssam M. A., editor.

Contributor:

Sims, Robert, 1975- editor.

Young, Amanda, 1986- editor.

Conference Name:

Arizona School of Analysis and Mathematical Physics (2018 : Tucson, Ariz.)

Series:

Contemporary mathematics (American Mathematical Society). 0271-4132 741

Contemporary mathematics, 741 0271-4132

Language:

English

Subjects (All):

Mathematical physics.

Mathematical analysis.

Physical Description:

1 online resource (210 pages).

Edition:

1st ed.

Place of Publication:

[Place of publication not identified] : American Mathematical Society, [2020]

Language Note:

English

Summary:

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.

Contents:

A class of two-dimensional AKLT models with a gap / Houssam Abdul-Rahman, Marius Lemm, Angelo Lucia, Bruno Nachtergaele, and Amanda Young

Note on linear response for interacting hall insulators / Sven Bachmann, Alex Bols, Wojciech De Roeck, and Martin Fraas

The adiabatic theorem in a quantum many-body setting / Sven Bachmann, Wojciech De Roeck, and Martin Fraas

Perspectives on exponential random graphs / Ryan DeMuse and Mei Yin

A Schrödinger operator approach to higher spin XXZ systems on general graphs / Christoph Fischbacher

An index theorem for Schrödinger operators on metric graphs / Yuri Latushkin and Selim Sukhtaiev

Finite-size criteria for spectral gaps in D-dimensional quantum spin systems / Marius Lemm

The KPZ universality class and related topics / Axel Saenz

Aspects of the mathematical theory of disordered quantum spin chains / Gunter Stolz.

Notes:

Description based on print version record.

"Arizona School of Analysis and Mathematical Physics, March 5-9, 2018, University of Arizona, Tucson, Arizona."

Includes bibliographical references.

ISBN:

9781470453886

1470453886