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Hard Ball Systems and the Lorentz Gas

  • L. A. Bunimovich
  • D. Burago
  • N. Chernov
  • E. G. D. Cohen
  • C. P. Dettmann
  • J. R. Dorfman
  • S. Ferleger
  • R. Hirschl
  • A. Kononenko
  • J. L. Lebowitz
  • C. Liverani
  • T. J. Murphy
  • J. Piasecki
  • H. A. Posch
  • N. Simányi
  • Ya. Sinai
  • D. Szász
  • T. Tél
  • H. van Beijeren
  • R. van Zon
  • J. Vollmer
  • L. S. Young
  • D. Szász

Part of the Encyclopaedia of Mathematical Sciences book series (EMS, volume 101)

Table of contents

  1. Front Matter
    Pages I-VIII
  2. Introduction

    1. Domokos Szász
      Pages 1-5
  3. Mathematics

    1. Front Matter
      Pages 7-7
    2. D. Burago, S. Ferleger, A. Kononenko
      Pages 9-27
    3. N. Chernov, L. S. Young
      Pages 89-120
    4. N. Chernov
      Pages 121-143
    5. L. A. Bunimovich
      Pages 145-178
    6. C. Liverani
      Pages 179-216
    7. J. L. Lebowitz, J. Piasecki, Ya. Sinai
      Pages 217-227
  4. Physics

  5. Appendix

    1. Front Matter
      Pages 419-419
  6. Back Matter
    Pages 447-458

About this book

Introduction

Hard Ball Systems and the Lorentz Gas are fundamental models arising in the theory of Hamiltonian dynamical systems. Moreover, in these models, some key laws of statistical physics can also be tested or even established by mathematically rigorous tools. The mathematical methods are most beautiful but sometimes quite involved. This collection of surveys written by leading researchers of the fields - mathematicians, physicists or mathematical physicists - treat both mathematically rigourous results, and evolving physical theories where the methods are analytic or computational. Some basic topics: hyperbolicity and ergodicity, correlation decay, Lyapunov exponents, Kolmogorov-Sinai entropy, entropy production, irreversibility. This collection is a unique introduction into the subject for graduate students, postdocs or researchers - in both mathematics and physics - who want to start working in the field.

Keywords

Lorentz gas correlation differential equation entropy ergodic theory of hyperbolic dynamical systems ergodicity hard ball systems nonequilibrium stationary states statistical physics

Authors and affiliations

  • L. A. Bunimovich
    • 1
  • D. Burago
    • 2
  • N. Chernov
    • 3
  • E. G. D. Cohen
    • 4
  • C. P. Dettmann
    • 5
  • J. R. Dorfman
    • 6
  • S. Ferleger
    • 7
  • R. Hirschl
    • 8
  • A. Kononenko
    • 9
  • J. L. Lebowitz
    • 10
  • C. Liverani
    • 11
  • T. J. Murphy
    • 12
  • J. Piasecki
    • 13
  • H. A. Posch
    • 14
  • N. Simányi
    • 15
  • Ya. Sinai
    • 16
  • D. Szász
    • 17
  • T. Tél
    • 18
  • H. van Beijeren
    • 19
  • R. van Zon
    • 20
  • J. Vollmer
    • 21
    • 22
  • L. S. Young
    • 23
  1. 1.Southeast Applied Analysis CenterGeorgia Institute of TechnologyAtlantaUSA
  2. 2.Department of MathematicsThe Pennsylvania State UniversityUniversity Park,USA
  3. 3.Department of MathematicsUniversity of Alabama at BirminghamBirminghamUSA
  4. 4.Laboratory of Theoretical PhysicsThe Rockefeller UniversityNew YorkUSA
  5. 5.Department of Mathematics, University WalkUniversity of BristolBristolUK
  6. 6.Institute for Physical Science and Technology, Department of PhysicsUniversity of MarylandCollege ParkUSA
  7. 7.Department of MathematicsSUNY at Stony BrookStony BrookUSA
  8. 8.Institute for Experimental PhysicsUniversity of ViennaViennaAustria
  9. 9.Renaissance Tech. Corp, 600 Rt. 25-A ESetanketUSA
  10. 10.Center for Mathematical Sciences ResearchPiscatawayUSA
  11. 11.Dipartimento di MatematicaUniversità di Roma II (Tor Vergata), Via della Ricerca ScientificaRomaItaly
  12. 12.Department of ChemistryUniversity of MarylandCollege ParkUSA
  13. 13.Institute of Theoretical PhysicsWarsaw UniversityWarsawPoland
  14. 14.Institute for Experimental PhysicsUniversity of ViennaViennaAustria
  15. 15.Department of Mathematics, Campbell HallUniversity of Alabama at BirminghamBirminghamUSA
  16. 16.Dept. of Mathematics, 708 Fine HallPrinceton UniversityPrincetonUSA
  17. 17.Institute of MathematicsBudapest University of Technology and EconomicsBudapestHungary
  18. 18.Institute for Theoretical PhysicsEötvös UniversityBudapestHungary
  19. 19.Institute for Theoretical PhysicsUniversity of Utrecht, Princetonplein 5UtrechtThe Netherlands
  20. 20.Institute for Theoretical PhysicsUniversity of Utrecht, Princetonplein 5UtrechtThe Netherlands
  21. 21.Fachbereich PhysikUniv.-GH EssenEssenGermany
  22. 22.Max-Planck-Institute for Polymer ResearchMainzGermany
  23. 23.Courant Institute of Mathematical SciencesNew YorkUSA

Editors and affiliations

  • D. Szász
    • 1
  1. 1.Institute of MathematicsBudapest University of Technology and EconomicsBudapestHungary

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-04062-1
  • Copyright Information Springer-Verlag Berlin Heidelberg 2000
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-08711-0
  • Online ISBN 978-3-662-04062-1
  • Series Print ISSN 0938-0396
  • Buy this book on publisher's site