2 research outputs found
Universality of Level Spacing Distributions in Classical Chaos
We suggest that random matrix theory applied to a classical action matrix can
be used in classical physics to distinguish chaotic from non-chaotic behavior.
We consider the 2-D stadium billiard system as well as the 2-D anharmonic and
harmonic oscillator. By unfolding of the spectrum of such matrix we compute the
level spacing distribution, the spectral auto-correlation and spectral
rigidity. We observe Poissonian behavior in the integrable case and Wignerian
behavior in the chaotic case. We present numerical evidence that the action
matrix of the stadium billiard displays GOE behavior and give an explanation
for it. The findings present evidence for universality of level fluctuations -
known from quantum chaos - also to hold in classical physics
Spectral Statistics in the Quantized Cardioid Billiard
The spectral statistics in the strongly chaotic cardioid billiard are
studied. The analysis is based on the first 11000 quantal energy levels for odd
and even symmetry respectively. It is found that the level-spacing distribution
is in good agreement with the GOE distribution of random-matrix theory. In case
of the number variance and rigidity we observe agreement with the random-matrix
model for short-range correlations only, whereas for long-range correlations
both statistics saturate in agreement with semiclassical expectations.
Furthermore the conjecture that for classically chaotic systems the normalized
mode fluctuations have a universal Gaussian distribution with unit variance is
tested and found to be in very good agreement for both symmetry classes. By
means of the Gutzwiller trace formula the trace of the cosine-modulated heat
kernel is studied. Since the billiard boundary is focusing there are conjugate
points giving rise to zeros at the locations of the periodic orbits instead of
exclusively Gaussian peaks.Comment: 20 pages, uu-encoded ps.Z-fil