**Contemporary Mathematics**

Volume: 552;
2011;
224 pp;
Softcover

MSC: Primary 35; 60; 81; 82; 15;

**Print ISBN: 978-0-8218-6898-0
Product Code: CONM/552**

List Price: $88.00

AMS Member Price: $70.40

MAA Member Price: $79.20

**Electronic ISBN: 978-0-8218-8231-3
Product Code: CONM/552.E**

List Price: $83.00

AMS Member Price: $66.40

MAA Member Price: $74.70

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# Entropy and the Quantum II

Share this page *Edited by *
*Robert Sims; Daniel Ueltschi*

The goal of the Entropy and the Quantum schools has been to introduce
young researchers to some of the exciting current topics in mathematical
physics. These topics often involve analytic techniques that can easily
be understood with a dose of physical intuition.

In March of 2010, four beautiful lectures were delivered on the
campus of the University of Arizona. They included Isoperimetric
Inequalities for Eigenvalues of the Laplacian by Rafael Benguria,
Universality of Wigner Random Matrices by Laszlo Erdős, Kinetic
Theory and the Kac Master Equation by Michael Loss, and Localization
in Disordered Media by Günter Stolz. Additionally, there were
talks by other senior scientists and a number of interesting
presentations by junior participants. The range of the subjects and
the enthusiasm of the young speakers are testimony to the great
vitality of this field, and the lecture notes in this volume reflect
well the diversity of this school.

#### Readership

Graduate students and research mathematicians interested in mathematical physics and analysis.

# Table of Contents

## Entropy and the Quantum II

- Contents iii4 free
- Preface v6 free
- List of Participants vii8 free
- Kinetic Theory and the Kac Master Equation 110 free
- Isoperimetric Inequalities for Eigenvalues of the Laplacian 2130
- 1. Introduction 2231
- 2. Lecture 1: Can one hear the shape of a drum? 2332
- 3. Lecture 2: Rearrangements and the Rayleigh–Faber–Krahn Inequality 3140
- 4. Lecture 3: The Szegö–Weinberger and the Payne–Polya–Weinberger inequalities 4049
- 5. Lecture 4: Fourth order differential operators 5261
- 6. Appendix 5564
- References 5665

- Max-to-Mean Ratio Estimates for the Fundamental Eigenfunction of the Dirichlet Laplacian 6170
- An Introduction to the Mathematics of Anderson Localization 7180
- Schrödinger Operators with Potential V (n) = n−γ cos(2πnρ) 109118
- Random Unitary Models and their Localization Properties 117126
- Universality of Correlations for Random Analytic Functions 135144
- A Wegner Estimate for Wigner Matrices 145154
- Lieb-Robinson Bounds and Existence of the Thermodynamic Limit for a Class of Irreversible Quantum Dynamics 161170
- Quantum Heisenberg Models and their Probabilistic Representations 177186