33,125 research outputs found
On the decay of correlations in Sinai billiards with infinite horizon
We compute the decay of the autocorrelation function of the observable
in the Sinai billiard and of the observable in the associated
Lorentz gas with an approximation due to Baladi, Eckmann and Ruelle. We
consider the standard configuration where the disks is centered inside a unit
square. The asymptotic decay is found to be . An explicit
expression is given for the prefactor as a function of the radius of the
scatterer. For the small scatterer case we also present expressions for the
preasymptotic regime. Our findings are supported by numerical computations.Comment: 6 pages LaTeX, 5 postscript figure
Geometric phases and anholonomy for a class of chaotic classical systems
Berry's phase may be viewed as arising from the parallel transport of a
quantal state around a loop in parameter space. In this Letter, the classical
limit of this transport is obtained for a particular class of chaotic systems.
It is shown that this ``classical parallel transport'' is anholonomic ---
transport around a closed curve in parameter space does not bring a point in
phase space back to itself --- and is intimately related to the Robbins-Berry
classical two-form.Comment: Revtex, 11 pages, no figures
Bifurcations and Complete Chaos for the Diamagnetic Kepler Problem
We describe the structure of bifurcations in the unbounded classical
Diamagnetic Kepler problem. We conjecture that this system does not have any
stable orbits and that the non-wandering set is described by a complete trinary
symbolic dynamics for scaled energies larger then .Comment: 15 pages PostScript uuencoded with figure
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