Encyclopaedia of Mathematical Sciences

Hard Ball Systems and the Lorentz Gas

Authors: Bunimovich, L.A., Burago, D., Chernov, N., Cohen, E.G.D., Dettmann, C.P., Dorfman, J.R., Ferleger, S., Hirschl, R., Kononenko, A., Lebowitz, J.L., Liverani, C., Murphy, T.J., Piasecki, J., Posch, H.A., Simanyi, N., Sinai, Y., Szasz, D., Tel, T., Beijeren, H. van, Zon, R. van, Vollmer, J., Young, L.S.

Editors: Szasz, D. (Ed.)

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About this book

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.

Reviews

"... The reviews have been written for a non-specialist mature audience and are quite accessible, even in the first part. The bibliography is very generous. Overall, the book constitutes an excellent introduction into this active, sometimes controversial, field. Anybody interested in the recent advances of dynamical systems theory applied to non-equilibrium statistical mechanics will find this book of use. ..."

Daniel Wójcik, Pure and Applied Geophysics 160, p. 1376-1378, 2003


Table of contents (14 chapters)

  • Introduction

    Szász, Domokos

    Pages 1-5

  • A Geometric Approach to Semi-Dispersing Billiards

    Burago, D. (et al.)

    Pages 9-27

  • On the Sequences of Collisions Among Hard Spheres in Infinite Space

    Murphy, T. J. (et al.)

    Pages 29-49

  • Hard Ball Systems and Semi-Dispersive Billiards: Hyperbolicity and Ergodicity

    Simányi, N.

    Pages 51-88

  • Decay of Correlations for Lorentz Gases and Hard Balls

    Chernov, N. (et al.)

    Pages 89-120

Buy this book

eBook $149.00
price for USA (gross)
  • ISBN 978-3-662-04062-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $189.00
price for USA
  • ISBN 978-3-540-67620-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $189.00
price for USA
  • ISBN 978-3-642-08711-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Hard Ball Systems and the Lorentz Gas
Authors
Editors
  • D. Szasz
Series Title
Encyclopaedia of Mathematical Sciences
Series Volume
101
Copyright
2000
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-662-04062-1
DOI
10.1007/978-3-662-04062-1
Hardcover ISBN
978-3-540-67620-1
Softcover ISBN
978-3-642-08711-0
Series ISSN
0938-0396
Edition Number
1
Number of Pages
VIII, 458
Number of Illustrations and Tables
93 b/w illustrations, 5 illustrations in colour
Topics