Spectral theory and mathematical physics part 1 : a Festschrift in honor of Barry Simon's 60th birthday : a conference on spectral theory and mathematical physics in honor of Barry Simon's 60th birthday March 27-31 2006, California Institute of Technology Pasadena, California

Description

This Festschrift had its origins in a conference called SimonFest held at Caltech, March 27-31, 2006, to honor Barry Simon's 60th birthday. It is not a proceedings volume in the usual sense since the emphasis of the majority of the contributions is on reviews of the state of the art of certain fields, with particular focus on recent developments and open problems. The bulk of the articles in this Festschrift are of this survey form, and a few review Simon's contributions to a particular area. Part 1 contains surveys in the areas of Quantum Field Theory, Statistical Mechanics, Nonrelativistic Two-Body and $N$-Body Quantum Systems, Resonances, Quantum Mechanics with Electric and Magnetic Fields, and the Semiclassical Limit. Part 2 contains surveys in the areas of Random and Ergodic Schrödinger Operators, Singular Continuous Spectrum, Orthogonal Polynomials, and Inverse Spectral Theory. In several cases, this collection of surveys portrays both the history of a subject and its current state of the art. Exhaustive lists of references enhance the presentation offered in these surveys. A substantial part of the contributions to this Festschrift are survey articles on the state of the art of certain areas with special emphasis on open problems. This will benefit graduate students as well as researchers who want to get a quick, yet comprehensive introduction into an area covered in this volume Content: ""Contents"" ""Part 1. Quantum Field Theory, Statistical Mechanics, and Nonrelativistic Quantum Systems"" ""Preface"" ""A Mathematical Genealogy"" ""A Selection of Barry Stories"" ""Quantum Field Theory, Statistical Mechanics"" ""Perspectives in Statistical Mechanics"" ""Coherent Infrared Representations in Non-Relativistic QED"" ""Quantum Spin Systems After DLS 1978"" ""Barry Simon's Contributions to Quantum Field Theory"" ""Nonrelativistic Two-Body and N-Body Quantum Systems, Resonances"" ""Isoperimetric Inequalities for Eigenvalues of the Laplacian"" ""Non-Self-Adjoint Operators and Pseudospectra""""Barry Simon's Contributions to Non-Relativistic Quantum Mechanics: Two-Body and N-Body Schrödinger Operators and Resonances"" ""N-Body Quantum Scattering and Quantum Resonances: An Overview"" ""Mathematical Analysis of Bornâ€?Oppenheimer Approximations"" ""Perturbation Theory and Atomic Resonances Since Schrödinger's Time"" ""On a Theorem for Quantum Mechanical Scattering Theory"" ""Analytic Criteria in the Qualitative Spectral Analysis of the Schrödinger Operator"" ""The Spectral Geometry of Geometrically Finite Hyperbolic Manifolds """"Topics in the Theory of Positive Solutions of Second-Order Elliptic and Parabolic Partial Differential Equations"" ""Complex Scaling in Atomic Physics: A Staging Ground for Experimental Mathematics and for Extracting Physics from Otherwise Impossible Computations"" ""Recent Results on the Betheâ€?Sommerfeld Conjecture"" ""Electric and Magnetic Fields, Semiclassical Limit"" ""Recent Developments in Quantum Mechanics with Magnetic Fields"" ""Aspects of the Integer Quantum Hall Effect""