An Exactly Solvable Lorentz Gas
Author | : David John Gates |
Publisher | : |
Total Pages | : 23 |
Release | : 1974 |
Genre | : Diffusion |
ISBN | : 9780868900049 |
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Author | : David John Gates |
Publisher | : |
Total Pages | : 23 |
Release | : 1974 |
Genre | : Diffusion |
ISBN | : 9780868900049 |
Author | : D. Szasz |
Publisher | : Springer Science & Business Media |
Total Pages | : 458 |
Release | : 2013-12-11 |
Genre | : Mathematics |
ISBN | : 366204062X |
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.
Author | : Ladislaus Alexander Banyai |
Publisher | : World Scientific |
Total Pages | : 283 |
Release | : 2020-07-30 |
Genre | : Science |
ISBN | : 9811223823 |
This book discusses in depth many of the key problems in non-equilibrium physics. Besides the standard subjects (Boltzmann and Master equations, linear response) it includes several new important subjects as well. The origin of macroscopic irreversible (dissipative) behavior receives an extended attention and is illustrated in the framework of solvable classical models of open systems (Chapter 3). The scaling relationship between the kinetic and hydrodynamical levels is described in Chapter 9. The QED of charged non-relativistic particles and its restriction to the states without photons to order 1/c² leading to the current-current magnetic interaction is discussed in some depth in Chapters 14 and 15. Bose-Einstein condensation in real time within the frame of rate equations, as well as soliton-like solutions of the non-linear Gross-Pitaevskii equation are discussed in Chapter 22. The presentation also includes the latest developments — quantum kinetics — related to modern ultrafast spectroscopy (Chapters 23-30).This second edition was improved, restructured, and enriched with new results from the recent papers of the author. Chapter 3 was largely extended and Chapters 14 and 15 are completely new. Chapter 22 has a new Section. Several new useful figures were added throughout the book as well.
Author | : Ilya Prigogine |
Publisher | : John Wiley & Sons |
Total Pages | : 475 |
Release | : 2009-09-09 |
Genre | : Science |
ISBN | : 0470142111 |
In Resonances, Instability, and Irreversibility: The LiouvilleSpace Extension of Quantum Mechanics T. Petrosky and I. Prigogine Unstable Systems in Generalized Quantum Theory E. C. G. Sudarshan, Charles B. Chiu, and G. Bhamathi Resonances and Dilatation Analyticity in Liouville Space Erkki J. Brandas Time, Irreversibility, and Unstable Systems in QuantumPhysics E. Eisenberg and L. P. Horwitz Quantum Systems with Diagonal Singularity I. Antoniou and Z. Suchanecki Nonadiabatic Crossing of Decaying Levels V. V. and Vl. V. Kocharovsky and S. Tasaki Can We Observe Microscopic Chaos in the Laboratory? Pierre Gaspard Proton Nonlocality and Decoherence in Condensed Matter --Predictions and Experimental Results C. A. Chatzidimitriou-Dreismann "We are at a most interesting moment in the history of science.Classical science emphasized equilibrium, stability, and timereversibility. Now we see instabilities, fluctuations, evolution onall levels of observations. This change of perspective requires newtools, new concepts. This volume invites the reader not to anenumeration of final achievements of contemporary science, but toan excursion to science in the making." --from the Foreword by I.Prigogine What are the dynamical roots of irreversibility? How can past andfuture be distinguished on the fundamental level of description?Are human beings the children of time --or its progenitors? Inrecent years, a growing number of chemists and physicists haveagreed that the solution to the problem of irreversibility requiresan extension of classical and quantum mechanics. There is, however,no consensus on which direction this extension should take toinclude the dynamical description of irreversible processes. Resonances, Instability, and Irreversibility surveys recentattempts --both direct and indirect --to address the problem ofirreversibility. Internationally recognized researchers report ontheir recent studies, which run the gamut from experimental tohighly mathematical. The subject matter of these papers falls intothree categories: classical systems with emphasis on chaos anddynamical instability, resonances and unstable quantum systems, andthe general problem of irreversibility. Presenting the cutting edge of research into some of the mostcompelling questions that face contemporary chemical physics,Resonances, Instability, and Irreversibility is fascinating readingfor professionals and students in every area of the discipline.
Author | : Da-Quan Jiang |
Publisher | : Springer Science & Business Media |
Total Pages | : 296 |
Release | : 2004 |
Genre | : Markov processes |
ISBN | : 9783540206118 |
Author | : Gerald T. Moore |
Publisher | : Springer Science & Business Media |
Total Pages | : 487 |
Release | : 2012-12-06 |
Genre | : Science |
ISBN | : 1461321816 |
The four-week period fran May 20 to June 16, 1984 was an intensive period of advanced study on the foundations and frontiers of nonequili brium statistical physics (NSP). During the first two weeks of this period, an advanced-study course on the "Foundations of NSP" was con ducted in Albuquerque under the sponsorship of the University of New Mexico Center for High-Technology Materials. This was followed by a two-week NATO Advanced Study Insti tute on the "Frontiers of NSP" in Santa Fe under the same directorship. Many Students attended both meetings. This book comprises proceedings based on those lectures and covering a broad spectrum of topics in NSP ranging fran basic problems in quantum measurement theory to analogies between lasers and Darwinian evolution. The various types of quantum distribution functions and their uses are treated by several authors. other tools of NSP, such as Langevin equations, Fokker-Planck equations, and master equations, are developed and applied to areas such as laser physics, plasma physics, Brownian motion, and hydrodynamic instabilities. The properties and experimental detection of squeezed states and antibunching are described, as well as experimental tests of the violation of Bell's inequality. Information theory, mean-field theory, reservoir theory, entropy maximization, and even a novel nonlinear generalization of quantum mechanics are used to discuss nonequilibrium phenanena and the approach toward thermodynamic equilibrium.
Author | : J. R. Dorfman |
Publisher | : Cambridge University Press |
Total Pages | : 303 |
Release | : 1999-08-28 |
Genre | : Science |
ISBN | : 0521655897 |
Introduction to applications and techniques in non-equilibrium statistical mechanics of chaotic dynamics.
Author | : Ioannis Antoniou |
Publisher | : Springer Science & Business Media |
Total Pages | : 341 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3642845703 |
"Solitons and Chaos" is a response to the growing interest in systems exhibiting these two complementary manifestations of nonlinearity. The papers cover a wide range of topics but share common mathematical notions and investigation techniques. An introductory note on eight concepts of integrability has been added as a guide for the uninitiated reader. Both specialists and graduate students will find this update on the state ofthe art useful. Key points: chaos vs. integrability; solitons: theory and applications; dissipative systems; Hamiltonian systems; maps and cascades; direct vs. inverse methods; higher dimensions; Lie groups, Painleve analysis, numerical algorithms; pertubation methods.
Author | : Gza Gyrgyi |
Publisher | : World Scientific |
Total Pages | : 608 |
Release | : 1992 |
Genre | : Science |
ISBN | : 9789810209384 |
This volume comprises about forty research papers and essays covering a wide range of subjects in the forefront of contemporary statistical physics. The contributors are renown scientists and leading authorities in several different fields. This book is dedicated to Pter Szpfalusy on the occasion of his sixtieth birthday. Emphasis is placed on his two main areas of research, namely phase transitions and chaotic dynamical systems, as they share common aspects like the applicability of the probabilistic approach or scaling behaviour and universality. Several papers deal with equilibrium phase transitions, critical dynamics, and pattern formation. Also represented are disordered systems, random field systems, growth processes, and neural network. Statistical properties of interacting electron gases, such as the Kondo lattice, the Wigner crystal, and the Hubbard model, are treated. In the field of chaos, Hamiltonian transport and resonances, strange attractors, multifractal characteristics of chaos, and the effect of weak perturbations are discussed. A separate section is devoted to selected mathematical aspects of dynamical systems like the foundation of statistical mechanics, including the problem of ergodicity, and rigorous results on quantum chaos.
Author | : Alwyn Scott |
Publisher | : Routledge |
Total Pages | : 2881 |
Release | : 2006-05-17 |
Genre | : Reference |
ISBN | : 1135455570 |
In 438 alphabetically-arranged essays, this work provides a useful overview of the core mathematical background for nonlinear science, as well as its applications to key problems in ecology and biological systems, chemical reaction-diffusion problems, geophysics, economics, electrical and mechanical oscillations in engineering systems, lasers and nonlinear optics, fluid mechanics and turbulence, and condensed matter physics, among others.