Spectral statistics
For classically integrable systems the spectral statistics
are expected to follow a Poissonian random process.
In contrast, for classically
chaotic systems random matrix statistics are expected.
One of the simplest statistics is the
level spacing distribution,
i.e. the distribution
of the spacings between neighboured eigenvalues.
For the integrable circular billiard and the strongly chaotic
cardioid billiard one gets:
However, both for integrable and chaotic systems exceptions are known.
Mode fluctuation distribution
The distribution for the (suitably) normalized fluctuations
of the spectral staircase function around its mean behaviour
has been conjectured to be Gaussian for strongly chaotic systems and
non-Gaussian otherwise.
The figure shows the mode fluctuation distribution
for the cardioid billiard and a rectangular billiard:
References:
Last modified: 27 October 2004, 16:21:54
Impressum, © Arnd Bäcker
