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Quantum Theory

Chaos. Program Collection for the PC by H.J. Korsch, H.-J. Jodl, T. Hartmann

By H.J. Korsch, H.-J. Jodl, T. Hartmann

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Best quantum theory books

Nature Loves to Hide: Quantum Physics and the Nature of Reality, a Western Perspective

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Contents:

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The name of Complementarity
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From a Universe of gadgets to a Universe of Experiences:
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For the case Tr L < −2, the eigenvalues can be written as λ± = −e∓γ , and the behavior is very similar except that the iterates alternate between both branches of the hyperbola. This is a ‘hyperbolic fixed point with reflection’ . (b) |Tr L| < 2 : The eigenvalues are complex conjugate and of unit absolute value. 100) where β is called the ‘stability angle’ . 101) ξ n = Ln ξ 0 = a+ e+inβ ξ + + a− e−inβ ξ − . 102) These iterates are all restricted to an ellipse, which is rotated in the (x, y)plane (see below) and the fixed point is called an ‘elliptic fixed point’ , as illustrated in Fig.

But, nevertheless, there are infinitely many of them. 0 1 1 6 5 1 7 1 4 1 3 2 7 2 5 1 2 3 7 3 5 4 7 2 3 3 4 5 7 1 4 1 5 6 ω1 / ω2 6 7 Fig. 4. 5 at rational frequency ratio r/s. 24) −5/2 −3/2 = K(ε) s . 23) goes to zero for ε → 0, so that for a sufficiently weak perturbation the phase space volume not filled with invariant curves can be made arbitrarily small. The invariant tori in the zones excluded by the KAM condition are in most cases destroyed. In the centers of the destroyed zone we have a torus with rational frequency ratio and, hence, periodic motion.

It should be Fig. 8. Dissipative flow in three-dimensional phase space converging to a strange attractor. 26 2 Nonlinear Dynamics and Deterministic Chaos noted that phase space trajectories can not cross and that the limiting set of this process will be a very complicated geometrical object. The process of stretching and folding can be illustrated by the ‘Smale horseshoe map’ [13]. The map consists of a stretching of a two-dimensional square followed by a folding over into the shape of a horseshoe, as illustrated in Fig.

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