- Autocorrelation function of eigenstates
in chaotic and mixed systems
- A. Bäcker and R. Schubert
J. Phys. A 35 (2002) 539-564
- We study the autocorrelation function of different types
of eigenfunctions in quantum mechanical systems with either chaotic
or mixed classical limits. We obtain an expansion of the
autocorrelation function in terms
of the correlation length.
For localized states, like bouncing ball modes or states
living on tori, a simple model using only classical
input gives good agreement with the exact result.
In particular, a prediction for irregular
eigenfunctions in mixed systems is derived and tested.
For chaotic systems, the expansion of the autocorrelation function
can be used to test quantum ergodicity on different length scales.
- Please refer to the above published version.
(The preprint version of this article can be obtained as
BRIMS Report HPL-BRIMS-00-11, April 2001, 30 pp.
(1.2 MB compressed, 5 MB uncompressed).)
For eigenfunctions which localize on an elliptic orbit
the expansion of the autocorrelation function gives
a prediction in the semiclassical limit:
For irregular states in mixed systems one obtains a prediction
for the autocorrelation function which is substantially
different from the J0(r)
in ergodic systems.
The figure below shows an eigenfunction in the
limaçon billiard (ε=0.3, approx 130516th
the corresponding Poincaré Husimi representation
and the classical angular momentum distribution and
finally the resulting autocorrelation function.
Thus, even for irregular states the autocorrelation function
clearly differs from the J0(r) behaviour!
Last modified: 27 October 2004, 16:21:49
Impressum, © Arnd Bäcker