DOCSLIB.ORG

Differential Equations and Mathematical Physics Proceedings

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Differential Equations and Mathematical Physics Proceedings Selected Titles in This Series 16 Rudi Weikard and Gilbert Weinstein, Editors, Differential Equations and Mathematical Physics, 2000 15 Ling Hsiao and Zhouping Xin, Editors, Some Current Topics on Nonlinear Conservation Laws, 2000 14 Jun-ichi Igusa, An Introduction to the Theory of Local Zeta Functions, 2000 13 Vasilios Alexiades and George Siopsis, Editors, Trends in Mathematical Physics, 1999 12 Sheng Gong, The Bieberbach Conjecture, 1999 11 Shinichi Mochizuki, Foundations of p-adic Teichmüller Theory, 1999 10 Duong H. Phong, Luc Vinet, and Shing-Tung Yau, Editors, Mirror Symmetry III, 1999 9 Shing-Tung Yau, Editor, Mirror Symmetry I, 1998 8 Jürgen Jost, Wilfrid Kendall, Umberto Mosco, Michael Röckner, and Karl-Theodor Sturm, New Directions in Dirichlet Forms, 1998 7 D. A. Buell and J. T. Teitelbaum, Editors, Computational Perspectives on Number Theory, 1998 6 Harold Levine, Partial Differential Equations, 1997 5 Qi-keng Lu, Stephen S.-T. Yau, and Anatoly Libgober, Editors, Singularities and Complex Geometry, 1997 4 Vyjayanthi Chari and Ivan B. Penkov, Editors, Modular Interfaces: Modular Lie Algebras, Quantum Groups, and Lie Superalgebras, 1997 3 Xia-Xi Ding and Tai-Ping Liu, Editors, Nonlinear Evolutionary Partial Differential Equations, 1997 2.2 William H. Kazez, Editor, Geometrie Topology, 1997 2.1 William H. Kazez, Editor, Geometrie Topology, 1997 1 B. Greene and S.-T. Yau, Editors, Mirror Symmetry II, 1997 This page intentionally left blank Differential Equations and Mathematical Physics This page intentionally left blank https://doi.org/10.1090/amsip/016 AM S/1 P Studies in Advanced Mathematics Volume 16 Differential Equations and Mathematical Physics Proceedings of an International Conference held at the University of Alabama in Birmingham, Maren 16-20, 1999 Rudi Weikard and Gilbert Weinstein, Editors American Mathematical Society · International Press Shing-Tung Yau, Managing Editor 2000 Mathematics Subject Classification. Primary 34-06, 35-06. Library of Congress Cataloging-in-Publication Data Differential equations and mathematical physics : proceedings of an international Conference held at the University of Alabama in Birmingham, March 16-20, 1999 / Rudi Weikard and Gilbert Weinstein, editors. p. cm. — (AMS/IP studies in advanced mathematics, ISSN 1089-3288 ; v. 16) Includes bibliographical references ISBN 0-8218-2157-1 1. Differential equations—Numerical Solutions—Congresses. 2. Mathematical physics— Congresses. I. Weikard, Rudi, 1958- IL Weinstein, Gilbert, 1957- III. International Con• ference on Differential Equations and Mathematical Physics (8th : 1999 : University of Alabama in Birmingham) IV. Series. QC20.7.D5D544 2000 515M5—dc21 00-025797 Copying and reprinting. Material in this book may be reproduced by any means for edu- cational and scientific purposes without fee or permission with the exception of reproduction by Services that collect fees for delivery of documents and provided that the customary acknowledg- ment of the source is given. This consent does not extend to other kinds of copying for general distribution, for advertising or promotional purposes, or for resale. Requests for permission for commercial use of material should be addressed to the Assistant to the Publisher, American Mathematical Society, P. O. Box 6248, Providence, Rhode Island 02940-6248. Requests can also be made by e-mail to [email protected]. Excluded from these provisions is material in articles for which the author holds Copyright. In such cases, requests for permission to use or reprint should be addressed directly to the author(s). (Copyright ownership is indicated in the notice in the lower right-hand corner of the first page of each article.) © 2000 by the American Mathematical Society and International Press. All rights reserved. The American Mathematical Society and International Press retain all rights except those granted to the United States Government. Printed in the United States of America. @ The paper used in this book is acid-free and falls within the guidelines established to ensure permanence and durability. Visit the AMS home page at URL: http://www.ams.org/ Visit the International Press home page at URL: http://www.intlpress.com/ 10 9 8 7 6 5 4 3 2 1 05 04 03 02 01 00 Contents Preface xi List of Plenary Speakers xiii List of Special Sessions xv List of Participants xvii A. A. BALINSKY AND W. D. EVANS On the Brown-Ravenhall Relativistic Hamiltonian and the Stability of Matter 1 ROBERT BARTNIK Assessing Accuracy in a Numerical Einstein Solver 11 RAFAEL D. BENGURIA AND M. CRISTINA DEPASSIER Variational Principle for the Limit Cycle of Rayleigh's Equation 21 BEVERLY K. BERGER Approach to the Singularity in Spatially Inhomogeneous Cosmologies 27 M. SH. BIRMAN AND T. A. SUSLINA On the Absolute Continuity of the Periodic Schrödinger and Dirac Operators with Magnetic Potential 41 T. BODINEAU AND Â. HELFFER Correlations, Spectral Gap, and Log-Sobolev Inequalities for Unbounded Spin Systems 51 RAYMOND BRUMMELHUIS, MARY BETH RUSKAI AND ELISABETH WERNER One Dimensional Regularizations of the Coulomb Potential with Application to Atoms in Strong Magnetic Fields 67 DONGHO CHAE AND OLEG YU. IMANUVILOV Construction of a Solution to the Semilinear Elliptic Equation in Chern-Simons Gauge Theory 77 viii CONTENTS Ì . CHRIST, Á. KISELEV AND Y. LAST Approximate Eigenvectors and Spectral Theory 85 DEMETRIOS CHRISTODOULOU The Initial Value Problem in the Large and Spacetime Singularities 97 LÄSZLO ERDÖS AND JAN PHILIP SOLOVEJ On the Kernel of Spinc Dirac Operators on §3 and R3 111 RICHARD FROESE AND IRA HERBST Realizing Holonomic Constraints in Classical and Quantum Mechanics 121 FRITZ GESZTESY AND HELGE HOLDEN Á Combined Sine-Gordon and Modified Korteweg-de Vries Hierarchy and its Algebro-geometric Solutions 133 M. GRIESEMER Á Minimax Principle for Eigenvalues in Spectral Gaps 175 GEORGE A. HAGEDORN AND ALAIN JOYE Semiclassical Dynamics and Exponential Asymptotics 181 RAINER HEMPEL AND KARSTEN LIENAU Genericity of the Band-Gap Structure of Periodic Media in the Large Coupling Limit 197 ANDREAS M. HINZ Distribution of Eigenvalues in the Dense Point Spectrum of Schrödinger Operators 207 P. D. HISLOP On the Distribution of Scattering Resonances for Asymptotically Hyperbolic Manifolds 217 THOMAS HUPFER, HAJO LESCHKE, AND SIMONE WARZEL The Multiformity of Lifshits Tails Caused by Random Landau Hamiltonians with Repulsive Impurity Potentials of Different Decay at Infinity 233 WITOLD KARWOWSKI AND VOLODYMYR KOSHMANENKO Schrödinger Operator Perturbed by Dynamics of Lower Dimension 249 YAROSLAV V. KURYLEV AND MATT! LASSAS Hyperbolic Inverse Problem with Data on a Part of the Boundary 259 YANYAN LI Best Sobolev Inequalities on Riemannian Manifolds 273 ELLIOTT H. LIEB AND MICHAEL LÖSS Self-Energy of Electrons in Non-Perturbative QED 279 ELLIOTT H. LIEB AND JAKOB YNGVASON The Ground State Energy of a Dilute Böse Gas 295 CONTENTS ix MAYUMI OHMIYA Trace Formulae and Completely Integrable Hamiltonians 307 YEHUDA PINCHOVER On the Maximum and Anti-maximum Principles 323 THOMAS C. SIDERIS The Null Condition and Global Existence of Nonlinear Elastic Waves 339 HEINZ SIEDENTOP The Hartree-Fock Approximation in Quantum Electrodynamics - Positivity of the Energy 347 J.A. SMOLLER AND J.B. TEMPLE Shock-Wave Cosmology 351 STEPHEN BRUCE SONTZ On Some Reverse Inequalities in the Segal-Â argmann Space 361 GERALD TESCHL On the Initial Value Problem of the Toda and Kac-van Moerbeke Hierarchies 375 V. TKACHENKO Á Class of Non-Selfadjoint HiH's Operators with Analytic Potentials 385 MICHAEL M. TOM Regularized Long Wave-KP Models 393 CHRISTIANE TRETTER Spectral Issues for Block Operator Matrices 407 JEFF A. VIACLOVSKY Some Fully Nonlinear Equations in Conformal Geometry 425 RICARDO WEDER LP — Lv Estimates for the Schrödinger Equation and Inverse Scattering 435 G. WOLANSKI Stationary States of Vlasov System 449 This page intentionally left blank Preface At which point do individual Conferences become a series? We think that the crucial element to look for is whether the participants naturally expect the next Conference, and — preferably — also look forward to it. In this respect, we certainly hope that the UAB-GIT Conferences have long become a series. Thus, we would for the most part only be repeating prefaces to previous volumes, were we to describe the purpose, scope, and contents of this Conference, the 8th Inter• national Conference on Differential Equations and Mathematical Physics, held in Birmingham, Alabama, March 16-20, 1999. It should nevertheless be noted that this Conference series started in 1981 as a meeting on spectral and scattering the- ory with 90 participants from North America and Europe. It has since grown, not only in the number of participants and countries, but also by encompassing many other disciplines, such as Statistical physics, general relativity, geometric analysis, fluid dynamics, and elasticity, among others. This Conference featured 172 talks, and was attended by over 200 participants from 25 countries: Australia (2), Aus- tria (3), Canada (6), Chile (4), the Czech Republic (2), Denmark (2), Egypt (1), Finland (3), France (7), Germany (24), Israel (7), Italy (3), Japan (10), Mexico (7), Norway (2), Poland (1), PR China (1), Russia (5), South Korea (1), Sweden (5), Switzerland (1), Turkey (1), United Kingdom (11), Ukraine (2), United States (95). Previous Conferences in the series were held in Birmingham in 1981, 1983, 1986, 1990, 1994, as well as in Atlanta in 1992, and 1997. We attempted to run an entirely
Load more

Recommended publications
  • Jan Philip Solovej CV (April 2021)
    Jan Philip Solovej CV (April 2021) Personal: Workplace: Professor Jan Philip Solovej Institute for Mathematical Sciences Born: June 14, 1961, Copenhagen, Denmark University of Copenhagen Citizenship: Danish Universitetsparken 5 Married, two Children DK-2100 Copenhagen, DENMARK http://www.math.ku.dk/∼solovej Email: [email protected] Education: • Cand. Scient., University of Copenhagen, 1985 • Ph.D., Princeton University, 1989 Research interests: Mathematical Physics: Stability of Matter, Many-body theory, Atomic structure, Bose gases, Condensed matter Physics, Statistical mechanics, Semiclassics, Varia- tional methods, Spectral theory, Partial differential equations, Quantum Information Theory Employment: • 1989-90: Visiting Assistant Professor, Dept. of Math., University of Michigan • 1990 (Fall): Post-doctoral fellow, Dept. of Math., University of Toronto • 1991 (Spring): Member, School of Math., Institute for Advanced Study, Princeton • 1991-1995: Assistant Professor, Dept. of Math., Princeton University • 1995-1997: Research Professor (Forskningsprofessor), Dept. of Math., Aarhus Univ. • 1997-present: Professor, Inst. for Math. Sciences, University of Copenhagen • 2016-2026: Centre leader: VILLUM Centre of Excellence for the Mathematics of Quantum Theory (QMATH). Visiting Positions: • 1997 (Spring): Member, School of Math., Institute for Advanced Study, Princeton • 2003-2004: Member, School of Math., Institute for Advanced Study, Princeton • 2004 (2 months) Visitor Dept. of Physics, Princeton University • 2005 (1 month) Visiting Professor, Universit´eParis Dauphine • 2007 (Spring) Mercator Guest Professor, Ludwig-Maximilians-Universit¨at,M¨unchen 1 • 2013 (1 month) Visiting Professor Universit´eParis 6 • 2014 (3 months) Senior Research Fellow, Erwin Schr¨odingerInstitute, Vienna • 2020 (1 month) Visiting Professor, IST Austria Honors • Member of the The Royal Danish Academy of Sciences and Letters (elected 2000) • The 2001 University of Copenhagen Teacher of the Year Award • The 2002 Friedman Rescue Award for significant contributions to Mathematical Physics.
    [Show full text]
  • Niels Bohr International Academy Annual Report 2015
    Niels Bohr International Academy Annual Report 2015 Contact Anette Studsgård Administrative coordinator [email protected] +45 3533 7870 2 Table of Contents NBIA Board and Director’s Council 4 From the Director 6 From the Board Chairman 8 From the Council Chairman 9 The NBIA in 2015 10 NBIA Colloquia and talks 21 Public Outreach 23 NBIA Faculty 24 Junior Faculty 32 Postdoctoral Fellows 38 Visiting Professors 42 PhD Students 44 MSc Students 45 Administrative Staff 46 Visitors 2015 47 Publications 2015 51 Workshops and PhD Schools 2015 63 NBIA Colloquia 64 3 Scientific Advisory Board Andrew D. Jackson, Niels Bohr Institute (Chairman) David Gross, KITP Santa Barbara Charles Marcus, Niels Bohr Institute Itamar Procaccia, Weizmann Institute Herbert Spohn, TU Munich Paul Steinhardt, Princeton University Frank Wilczek, MIT 4 Director’s Council Lars Kann-Rasmussen (Chairman) Connie Hedegaard Niels Due Jensen Per Magid Bjørn Nørgaard Michael Rasmussen 5 From the Director When the Niels Bohr International Academy (NBIA) started in 2007 we were literally three faculty members and around four post-docs. Things moved fast, and at the five- anniversary of the NBIA in 2012 we put to- gether a five-year report that showed the remarkable scientific quality and breadth that had been achieved. Today, our level of activi- ties are at a scale where we no longer fit into the building originally assigned to us. Slowly, office space in the main building of the Niels Bohr Institute on Blegdamsvej is now also becoming part of the NBIA. However, growth is not only in the number of scientist who work here, or who visit us.
    [Show full text]
  • 10Th St. Petersburg Conference in Spectral Theory Programme And
    Euler International Mathematical Institute St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences 10th St. Petersburg Conference in Spectral Theory 9 { 12 June 2018 Dedicated to the memory of M. Sh. Birman (1928 { 2009) Supported by Russian Foundation of Basic Research, grant no. 18-01-20034-g Chebyshev Laboratory (St. Petersburg State University) Simons Foundation (via PDMI RAS, grant no. 507309) Programme and abstracts St. Petersburg, 2018 Organizers: Alexandre Fedotov, Nikolai Filonov, Alexander Sobolev, Tatyana Suslina, Dmitri Yafaev Organizing Committee: Alexandre Fedotov, Nikolai Filonov, Alexander Sobolev, Tatyana Suslina, Dmitri Yafaev, Ilya Kachkovskiy, Tatyana Vinogradova, Nadia Zalesskaya 10th St. Petersburg Conference in Spectral Theory. Proceedings of the conference. Euler International Mathematical Institute, St. Petersburg, 2018. The Conference was organized at Euler International Mathematical Institute which is a part of St. Petersburg Department of Steklov Institute of Mathematics. The organizers are grateful to the staff of Euler and Steklov Institutes for their help and support. The 10th St. Petersburg Conference in Spectral Theory is supported by Russian Foundation of Basic Research, grant 18-01-20034-g, and by Chebyshev Laboratory (St. Petersburg State University, Russia). Conference website: http://www.pdmi.ras.ru/EIMI/2018/ST/index.html 2 Speakers • Alexander APTEKAREV, Keldysh Institute of Applied Mathematics, Russia • Roman BESSONOV, St. Petersburg State University and PDMI RAS, Russia • Nikolay FILONOV, PDMI RAS, Russia • Alexander GRIGORIAN, Bielefeld University, Germany • Alexander ITS, Indiana University { Purdue University Indianapolis, USA • Victor IVRII, University of Toronto, Canada • Fr´ed´ericKLOPP, Universit´ePierre et Marie Curie, Paris • Aleksey KOSTENKO, Universit¨atWien, Austria, and University of Ljubljana, Slovenia • Andrei Mart´ınezFILKENSTEIN, Universidad de Almer´ıa,Spain • Boris MITYAGIN, Ohio State University, USA • Sergei NAZAROV, St.
    [Show full text]
  • QMATH14: Mathematical Results in Quamtum Physics – Abstracts
    QMath14: Mathematical Results in Quantum Physics Aarhus University, 12–16 August 2019 Programme and abstracts – including posters Programme . .next page Abstracts . page 18 Posters . page 63 http://conferences.au.dk/qmath14/ Last update: 2019-08-13 09:53:41 Foto: Anders Trærum, AU Communication Programme Monday, 12 August 09:00–12:00 Mini course A quantum information travel guide for mathematicians Lecturer: David Pérez García Location: Aud E (1533.103) 12:00–14:00 Lunch Location: MATH Canteen (1536, ground floor) 14:00–15:00 Plenary talk Zeno and the bomb Michael Wolf Chair: Pavel Exner Location: Aud E (1533.103) 15:00–15:30 Coffee break 15:30–16:30 Plenary talk An update on Many-Body Localization Wojciech De Roeck Chair: Pavel Exner Location: Aud E (1533.103) 16:30–17:00 Break 17:00– Welcome reception 1 Tuesday, 13 August 09:30–10:30 Plenary talk Quantized quantum transport in interacting systems Sven Bachmann Chair: Simone Warzel Location: Aud E (1533.103) 10:30–11:00 Break 11:00–12:00 Plenary talk Universal Singularities of Random Matrices Torben Krüger Chair: Simone Warzel Location: Aud E (1533.103) 12:00–14:00 Lunch Location: MATH Canteen (1536, ground floor) 14:00–15:30 Parallel sessions – Main speakers Spectral Theory in Aud F (1534.125) see page 8 Quantum Information in Aud G1 (1532.116) see page 9 Many-Body Systems in Aud G2 (1532.122) see page 10 Random Systems in Koll G3 (1532.218) see page 11 Condensed Matter in Koll G4 (1532.222) see page 12 15:30–16:00 Coffee break 2 16:00–17:55 Parallel sessions – Contributed speakers Spectral
    [Show full text]
  • Derivation of Ginzburg-Landau Theory for a One-Dimensional System With
    DERIVATION OF GINZBURG-LANDAU THEORY FOR A ONE-DIMENSIONAL SYSTEM WITH CONTACT INTERACTION RUPERT L. FRANK, CHRISTIAN HAINZL, ROBERT SEIRINGER, AND JAN PHILIP SOLOVEJ Abstract. In a recent paper [7] we give the first rigorous derivation of the cel- ebrated Ginzburg-Landau (GL) theory, starting from the microscopic Bardeen- Cooper-Schrieffer (BCS) model. Here we present our results in the simplified case of a one-dimensional system of particles interacting via a δ-potential. 1. Introduction and Main Results 1.1. Introduction. In 1950 Ginzburg and Landau [1] presented the first satis- factory mathematical description of the phenomenon of superconductivity. Their model examined the macroscopic properties of a superconductor in a phenomeno- logical way, without explaining its microscopic mechanism. In the GL theory the superconducting state is represented by a complex order parameter ψ(x), which is zero in the normal state and non-zero in the superconducting state. The order parameter ψ(x) can be considered as a macroscopic wave-function whose square ψ(x) 2 is proportional to the density of superconducting particles. | In| 1957 Bardeen, Cooper and Schrieffer [2] formulated the first microscopic ex- planation of superconductivity starting from a first principle Hamiltonian. In a major breakthrough they realized that this phenomenon can be described by the pairing-mechanism. The superconducting state forms due to an instability of the normal state in the presence of an attraction between the particles. In the case of a metal the attraction is made possible by an interaction through the lattice. For other systems, like superfluid cold gases, the interaction is of local type.
    [Show full text]
  • IAMP News Bulletin January 2020
    IAMP News Bulletin January 2020 International Association of Mathematical Physics Contents International Association of Mathematical Physics News Bulletin, January 2020 Contents Mathematical Physics at Matematisk Institut, Aarhus Universitet, 1954–20043 The Dannie Heineman Prize 11 IUPAP Conference Sponsorship 13 News from the IAMP Executive Committee 13 Contact coordinates for this issue 16 Bulletin Editor Editorial Board Evans Harrell Rafael Benguria, Yasuyuki Kawahigashi, Manfred Salmhofer, Robert Sims Contacts. http://www.iamp.org and e-mail: [email protected] Cover picture: Svetlana Jitomirskaja (picture courtesy of Tatiana Arizaga / UCI) M Φ The views expressed in this IAMP News Bulletin are those of the authors and do not necessarily represent those of the IAMP Executive Committee, Editor or Editorial Board. Any complete or partial performance or reproduction made without the consent of the author or of his successors in title or assigns shall be unlawful. All reproduction rights are henceforth reserved, and mention of the IAMP News Bulletin is obligatory in the reference. (Art.L.122-4 of the Code of Intellectual Property). ISSN 2304-7348 News Bulletin (International Association∩ of Mathematical Physics) 2 IAMP News Bulletin, January 2020 Mathematical Physics at Matematisk Institut, Aarhus Universitet, 1954–2004 Mathematical Physics at Matematisk Institut, Aarhus Univer- sitet,11954{2004 by SØREN FOURNAIS,ARNE JENSEN, and JACOB SCHACH MØLLER Introduction The Mathematics Institute, Aarhus University, Denmark, has played a significant role in devel- oping mathematical physics, both in Denmark, and in a wider international context. We will describe some of the activities and people in mathematical physics at Aarhus Uni- versity during the period 1954 to 2004.
    [Show full text]
  • Arxiv:Math-Ph/0507049V1 19 Jul 2005
    Ground-State Energy of a Dilute Fermi Gas Elliott H. Lieb, Robert Seiringer, and Jan Philip Solovej Abstract. Recent developments in the physics of low density trapped gases make it worthwhile to verify old, well known results that, while plausible, were based on perturbation theory and assumptions about pseudopotentials. We use and extend recently developed techniques to give a rigorous derivation of the asymptotic formula for the ground state energy of a dilute gas of N fermions interacting with a short-range, positive potential of scattering length a. For spin 1/2 fermions, this is E ∼ E0 + (~2/2m)2πNρa, where E0 is the energy of the non-interacting system and ρ is the density. 1. Introduction Our goal is to find the ground state energy of a low density gas of fermions interacting with short range pair potentials. Earlier [1, 2, 3, 4], the corresponding problem for bosons had been solved in the sense that the ‘well known’ ancient formula E/V = 4πρ2a in 3D was proved rigorously as an asymptotic formula for small ρ in the thermodynamic limit. Here, ρ = N/V , where N is the particle number, V is the volume and a is the scattering length of the pair potential. Owing to the recent interest in low density, cold gases of fermionic atoms, the 1 natural question arose: Is a similar formula valid for spin- 2 fermions? Of course there will be differences, which we can list as follows: (1) We can expect that the interaction energy between pairs of fermions of arXiv:math-ph/0507049v1 19 Jul 2005 the same spin vanishes to leading order in ρ.
    [Show full text]