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Hard Ball Systems and the Lorentz Gas

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Hard Ball Systems and the Lorentz Gas Cover

 

Synopses & Reviews

Publisher Comments:

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.

Table of Contents

Part I. Mathematics: 1. D. Burago, S. Ferleger, A. Kononenko: A Geometric Approach to Semi-Dispersing Billiards.- 2. T. J. Murphy, E. G. D. Cohen: On the Sequences of Collisions Among Hard Spheres in Infinite Spacel- 3. N. Simanyi: Hard Ball Systems and Semi-Dispersive Billiards: Hyperbolicity and Ergodicity.- 4. N. Chernov, L.-S. Young: Decay of Correlations for Lorentz Gases and Hard Balls.- 5. N. Chernov: Entropy Values and Entropy Bounds.- 6. L. A. Bunimovich: Existence of Transport Coefficients.- 7. C. Liverani: Interacting Particles.- 8. J. L. Lebowitz, J. Piasecki and Ya. G. Sinai: Scaling Dynamics of a Massive Piston in an Ideal Gas .- Part II. Physics: 1. H. van Beijeren, R. van Zon, J. R. Dorfman: Kinetic Theory Estimates for the Kolmogorov-Sinai Entropy, and the Largest Lyapunov Exponents for Dilute, Hard-Ball Gases and for Dilute, Random Lorentz Gases.- 2. H. A. Posch and R. Hirschl: Simulation of Billiards and of Hard-Body Fluids.- 3. C. P. Dettmann: The Lorentz Gas: a Paradigm for Nonequilibrium Stationary States.- 4. T. Tl, J. Vollmer: Entropy Balance, Multibaker Maps, and the Dynamics of the Lorentz Gas.- Appendix: 1. D. Szasz: Boltzmanns Ergodic Hypothesis, a Conjecture for Centuries?

Product Details

ISBN:
9783540676201
Other:
Szasz, D.
Publisher:
Springer
Author:
Hirschl, R.
Author:
Ya. Sinai
Author:
Burago, D.
Author:
Liverani, C.
Author:
Murphy, T. J.
Author:
Chernov, N.
Author:
Ferleger, S.
Author:
Cohen, E. G. D.
Author:
Kononenko, A.
Author:
Lebowitz, J.L.
Author:
Posch, H.A.
Author:
Tel, T.
Author:
Szasz, D.
Author:
Dettmann, C.P.
Author:
Beijeren, H. van
Author:
Piasecki, J.
Author:
Dorfman, J. R.
Author:
Vollmer, J.
Author:
Simanyi, N.
Author:
Bunimovich, L. a.
Author:
Zon, R. van
Author:
Sinai
Author:
Young, L. S.
Location:
Berlin, Heidelberg
Subject:
General
Subject:
Physics
Subject:
Mathematical Analysis
Subject:
Dynamics
Subject:
Hamiltonian systems
Subject:
Statistics
Subject:
Lorentz gas
Subject:
ergodic theory of hyperbolic dynamical systems
Subject:
hard ball systems
Subject:
nonequilibrium stationary states
Subject:
Probability Theory and Stochastic Processes
Subject:
Theoretical, Mathematical and Computational Physics
Subject:
Analysis
Subject:
Analysis Outstanding research in dynamical systems.
Subject:
Mathematics-Analysis General
Subject:
Mathematics
Subject:
B
Subject:
mathematics and statistics
Subject:
Distribution (Probability theory)
Subject:
Global analysis (Mathematics)
Copyright:
Edition Description:
Book
Series:
Encyclopaedia of mathematical sciences,
Series Volume:
101
Publication Date:
20010112
Binding:
HARDCOVER
Language:
English
Illustrations:
Yes
Pages:
466
Dimensions:
235 x 155 mm 951 gr

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