Statistical properties of high-lying chaotic eigenstates

Details Statistical properties of high-lying chaotic eigenstates Statistical properties of high-lying chaotic eigenstates

1995-01-02

arxiv.org/abs/chao-dyn/9501003v1

Nonlinear Sciences

Chaotic Dynamics

LaTex file 18 pages, 7 figures upon request J. Phys. A. Math. Gen. 27(1994) 5509-5523

Scientific paper

We study the statistical properties of the high-lying chaotic eigenstates (200,000 and above) which are deep in the semiclassical regime. The system we are analyzing is the billiard system inside the region defined by the quadratic (complex) conformal map of the unit disk as introduced by Robnik (1983). We are using Heller's method of plane wave decomposition of the numerical eigenfunctions, and perform extensive statistical analysis with the following conclusions: (1) The local average probability density is in excellent agreement with the microcanonical assumption and all statistical properties are also in excellent agreement with the Gaussian random model; \qquad (2) The autocorrelation function is found to be strongly direction dependent and only after averaging over all directions agrees well with Berry's (1977) prediction; \qquad (3) Although the scars of unstable classical periodic orbits (in such ergodic regime) are expected to exist, so far we have not found any (around 200,000th state) but a scar-like feature resembling the whispering gallery modes.

Affiliated with

Also associated with

No associations

Rating

Statistical properties of high-lying chaotic eigenstates does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Statistical properties of high-lying chaotic eigenstates, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Statistical properties of high-lying chaotic eigenstates will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-536416