Klaus Morawetz | PubMed Health

PubMed2003

Bifurcation in kinetic equation for interacting Fermi systems.

The recently derived nonlocal quantum kinetic equation for dense interacting Fermi systems combines time derivatives with finite time stepping known from the logistic mapping. This continuous delay differential equation is a consequence of the microscopic delay time representing the dynamics of the deterministic chaotic system. The responsible delay time is explicitly calculated and discussed for short-range correlations. As a novel feature oscillations in the time evolution of the distribution function itself appear and bifurcations up to chaotic behavior occur. The temperature and density conditions are presented where such oscillations and bifurcations arise indicating an onset of phase transition.

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PubMed2002

Relation between classical and quantum particle systems.

An exact correspondence is established between a N-body classical interacting system and a (N-1)-body quantum system with respect to the partition function. The resulting Hermitian quantum potential is a (N-1)-body one. Inversely the Kelbg potential is reproduced which describes quantum systems at a quasi-classical level. The correspondence found between classical and quantum systems allows also to approximate dense classical many-body systems by lower order quantum perturbation theory, replacing Planck's constant properly by temperature and density dependent expressions. As an example, the dynamical behavior of a one-component plasma is well reproduced concerning the formation of correlation energy after a disturbance, utilizing solely the analytical quantum-Born result for dense degenerated Fermi systems. As a practical guide, the quantum-Bruckner parameter r(s) has been replaced by the classical plasma parameter gamma as r(s) approximately 0.3gamma(3/2).

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