By R. Blümel, W. P. Reinhardt
The learn of chaos is this present day probably the most lively and prolific components in atomic physics. This ebook describes the manifestations of chaos in atoms and molecules, and is an creation to this attention-grabbing region. the 1st a part of the ebook bargains 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 ebook covers microwave-driven floor kingdom electrons, the hydrogen atom in a robust microwave box, the kicked hydrogen atom, chaotic scattering with CsI molecules and the helium atom. The ebook includes many diagrams and an in depth reference record.
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Extra resources for Chaos in Atomic Physics (Cambridge Monographs on Atomic, Molecular and Chemical Physics)
This system is obviously deterministic. Whenever the initial conditions XQ = x(t = 0) and VQ = v(t = 0) are known precisely, x(t) can be computed trivially for any t > 0. The answer is x(t) = vot + x0 mod 1. 1) But now Born argues that precise knowledge of XQ or VQ is not physical. No matter how good a measurement, there are always experimental uncertainties Axo and A^o in the initial position and the velocity that cannot be eliminated in principle. Even assuming no error in XQ, any uncertainty in VQ turns out to be disasterous for the long-term predictability of x(t) since there is always a time t = tc for which Ax = Avot becomes larger than 1.
We call it N2. The proof is the following: Assume that the set of functions / is of the same cardinality as the real numbers in [0,1]. Then, by the very definition of cardinality, a one-toone correspondence can be established between the functions / and the real numbers in [0,1]. In other words, the functions / can be "counted" introducing a continuous "counting label" x. Given an x G [0,1], there 36 2 Chaos: tools and concepts corresponds a fx(y) € F and vice versa. We will now show that no matter how ingeniously this counting scheme is set up, there is always a function g which does not belong to the scheme.
Quite generally the measure of a countable set is zero. This does not imply that the measure of an uncountable set is automatically nonzero. 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.