Geometrical approach for description of the mixed state in multi-well
potentials
release_fxod6if62vg3zanznordzvogl4
by
V.P.Berezovoj, Yu.L.Bolotin, G.I.Ivashkevych
2006
Abstract
We use so-called geometrical approach in description of transition from
regular motion to chaotic in Hamiltonian systems with potential energy surface
that has several local minima. Distinctive feature of such systems is
coexistence of different types of dynamics (regular or chaotic) in different
wells at the same energy Mixed state reveals unique opportunities in research
of quantum manifestations of classical stochasticity. Application of
traditional criteria for transition to chaos (resonance overlap criterion,
negative curvature criterion and stochastic layer destruction criterion) is
inefficient in case of potentials with complex topology. Geometrical approach
allows considering only configuration space but not phase space when
investigating stability. Trajectories are viewed as geodesics of configuration
space equipped with suitable metric. In this approach all information about
chaos and regularity consists in potential function. The aim of this work is to
determine what details of geometry of potential lead to chaos in Hamiltonian
systems using geometrical approach. Numerical calculations are executed for
potentials that are relevant with lowest umbilical catastrophes.
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