Tag: Deterministic

Free Download Mechanics: From Newton’s Laws to Deterministic Chaos by Florian A. Scheck
English | PDF | 1994 | 523 Pages | ISBN : 3540574751 | 38.2 MB
Purpose and Emphasis. Mechanics not only is the oldest branch of physics but was and still is the basis for all of theoretical physics. Quantum mechanics can hardly be understood, perhaps cannot even be formulated, without a good knowledge of general mechanics. Field theories such as electrodynamics borrow their formal framework and many of their building principles from mechanics. In short, throughout the many modem developments of physics where one fre quently turns back to the principles of c1assical mechanics its model character is feIt. For this reason it is not surprising that the presentation of mechanics reflects to some extent the development of modem physics and that today this c1assical branch of theoretical physics is taught rather differently than at the time of Arnold Sommerfeld, in the 1920s, or even in the 1950s, when more emphasis was put on the theory and the applications of partial-differential equations. Today, symme tries and invariance principles, the structure ofthespace-time continuum, and the geometrical structure of mechanics play an important role. The beginner should realize that mechanics is not primarily the art of describing block-and-tackles, coIIisions of billiard balls, constrained motions of the cylinder in a washing ma chine, or bicycle riding.

Free Download Mechanics: From Newton’s Laws to Deterministic Chaos, Third Edition by Florian A. Scheck
English | PDF | 1999 | 540 Pages | ISBN : 3540655581 | 41.5 MB
Purpose and Emphasis. Mechanics not only is the oldest branch of physics but was and still is the basis for all of theoretical physics. Quantum mechanics can hardly be understood, perhaps cannot even be formulated, without a good knowledge of general mechanics. Field theories such as electrodynamics borrow their formal framework and many of their building principles from mechanics. In short, throughout the many modern developments of physics where one frequently turns back to the principles of classical mechanics its model character is felt. For this reason it is not surprising that the presentation of mechanics reflects of modern physics and that today this classical to some extent the development branch of theoretical physics is taught rather differently than at the time of Arnold Sommerfeld, in the 1920s, or even in the 1950s, when more emphasis was put on the theory and the applications of partial-differential equations. Today, symmetries and invariance principles, the structure of the space-time continuum, and the geometrical structure of mechanics play an important role. The beginner should realize that mechanics is not primarily the art of describing block-and-tackles, collisions of billiard balls, constrained motions of the cylinder in a washing machine, or bicycle riding.

Free Download Deterministic Chaos in Infinite Quantum Systems by Fabio Benatti
English | PDF | 1993 | 229 Pages | ISBN : 3540570179 | 30.4 MB
The purpose of this volume is to give a detailed account of a series of re sults concerning some ergodic questions of quantum mechanics which have the past six years following the formulation of a generalized been addressed in Kolmogorov-Sinai entropy by A.Connes, H.Narnhofer and W.Thirring. Classical ergodicity and mixing are fully developed topics of mathematical physics dealing with the lowest levels in a hierarchy of increasingly random behaviours with the so-called Bernoulli systems at its apex showing a structure that characterizes them as Kolmogorov (K-) systems. It seems not only reasonable, but also inevitable to use classical ergodic theory as a guide in the study of ergodic behaviours of quantum systems. The question is which kind of random behaviours quantum systems can exhibit and whether there is any way of classifying them. Asymptotic statistical independence and, correspondingly, complete lack of control over the distant future are typical features of classical K-systems. These properties are fully characterized by the dynamical entropy of Kolmogorov and Sinai, so that the introduction of a similar concept for quantum systems has provided the opportunity of raising meaningful questions and of proposing some non-trivial answers to them. Since in the following we shall be mainly concerned with infinite quantum systems, the algebraic approach to quantum theory will provide us with the necessary analytical tools which can be used in the commutative context, too.