The analysis of quantum mechanical eigenfunctions in energy regimes where the classical motion is chaotic (Heller 1984, 1986 Founargio-takis, Farantos, Contopoulos, and Polymilis 1989). [Pg.188]

Gaspard and Rice have studied the classical, semiclassical and full quantum mechanical dynamics of the scattering of a point particle from three hard discs fixed in a plane (see Fig. 11). We note that the classical motion (which is chaotic) consists of trajectories which are trapped between the discs. [Pg.237]

The classical researches of Ludwig Boltzmann showed how this apparent contradiction could be explained, and how the mechanical theory of heat could be established on a firm basis, namely, by the hypothesis that heat consists of a chaotic (molecular ungeordnet) motion of the ultimate particles. [Pg.155]

Computational studies have indicated that chaotic behavior is expected in classical mechanical descriptions of the motion of highly excited molecules. As a consequence, intramolecular dynamics relates directly to the fundamental issues of quantum vs classical chaos and semiclassical quantization. Practical implications are also clear if classical mechanics is a useful description of intramolecular dynamics, it suggests that isolated-molecule dynamics is sufficiently complex to allow a statistical-type description in the chaotic regime, with associated relaxation to equilibrium, and a concomitant loss of controlled reaction selectivity. [Pg.126]

In contrast to dissipative dynamical systems, conservative systems preserve phase-space volumes and hence cannot display any attracting regions in phase space there can be no fixed points, no limit cycles and no strange attractors. There can nonetheless be chaotic motion in the sense that points along particular trajectories may show sensitivity to initial conditions. A familiar example of a conservative system from classical mechanics is that of a Hamiltonian system. [Pg.171]

It is fair to say that there has been a renaissance in the study of the properties of nonlinear dynamical systems in recent years.This work has brought forth the notion that the equations of classical mechanics describing most systems are fundamentally unsolvable, or nonintegrable, and that as a result all nonintegrable systems have universal scaling laws which underlie their complex and apparently chaotic motions. [Pg.117]

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