2 research outputs found
Nodal domains statistics - a criterion for quantum chaos
We consider the distribution of the (properly normalized) numbers of nodal
domains of wave functions in 2- quantum billiards. We show that these
distributions distinguish clearly between systems with integrable (separable)
or chaotic underlying classical dynamics, and for each case the limiting
distribution is universal (system independent). Thus, a new criterion for
quantum chaos is provided by the statistics of the wave functions, which
complements the well established criterion based on spectral statistics.Comment: 4 pages, 5 figures, revte
The leading Ruelle resonances of chaotic maps
The leading Ruelle resonances of typical chaotic maps, the perturbed cat map
and the standard map, are calculated by variation. It is found that, excluding
the resonance associated with the invariant density, the next subleading
resonances are, approximately, the roots of the equation , where
is a positive number which characterizes the amount of stochasticity
of the map. The results are verified by numerical computations, and the
implications to the form factor of the corresponding quantum maps are
discussed.Comment: 5 pages, 4 figures included. To appear in Phys. Rev.