By R. Blümel, W. P. Reinhardt
ISBN-10: 0511524501
ISBN-13: 9780511524509
ISBN-10: 0521017904
ISBN-13: 9780521017909
ISBN-10: 0521455022
ISBN-13: 9780521455022
The learn of chaos is this day the most energetic and prolific parts in atomic physics. This publication describes the manifestations of chaos in atoms and molecules, and is an creation to this interesting region. the 1st a part of the e-book offers with the speculation and ideas of classical chaos, that are then utilized to real atomic and molecular physics platforms within the moment a part of the booklet. The publication covers microwave-driven floor nation electrons, the hydrogen atom in a powerful microwave box, the kicked hydrogen atom, chaotic scattering with CsI molecules and the helium atom. The booklet comprises many diagrams and a close reference record.
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Extra info for Chaos in Atomic Physics (Cambridge Monographs on Atomic, Molecular and Chemical Physics)
Sample text
This was proved by means of a counterexample, again by Cantor. , where the digits aj are allowed to take only the values 0 and 2. 3). Geometrically, these numbers can be found in the interval [0,1] in a set which is constructed in the following way. Start with the interval [0,1] (see Fig. 2(a)). , where bj can be 0, 1 or 2). We obtain the set shown in Fig. 2(b). OI6364... ). The result is shown in Fig. 2(c). Continue this procedure ad infinitum. What is left in the end clearly has no extension.
The return map is one of the most useful tools for visualizing chaos in dynamical systems. We will encounter this mapping frequently in this book. 2 in connection with a physical system, the double pendulum. There are many special cases of orbits. 7) f(x0) = x0. For example, XQ = 1 — 1/r is a fixed point of the logistic map fr. The fixed point is a special type of periodic orbit. Suppose that for a particular mapping function / we have xi = f(x0)] x2 = f(x{) = x0. 9) a periodic orbit of period 2.
The proof of this fact is very difficult, but was produced toward the end of the last century. Irrationals which are not algebraic are called transcendental The transcendentals are not countable. The transcendentals are what remain of the real numbers after removing the rationals and the algebraic irrationals. Since the real numbers are not countable, but both rationals and algebraic irrationals are, the transcendentals are obviously not countable. Technically it is the existence of transcendental numbers in the number continuum that makes chaos possible.
Chaos in Atomic Physics (Cambridge Monographs on Atomic, Molecular and Chemical Physics) by R. Blümel, W. P. Reinhardt
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