Publication details
- Title:
- Chaotic eigenfunctions in momentum space
- Authors:
- A. Bäcker and R. Schubert
- Journal:
-
J. Phys. A 32 (1999) 4795-4815
- Abstract:
- We study eigenstates of chaotic billiards
in the momentum representation and propose the radially integrated momentum
distribution as useful measure to detect localization effects.
For the momentum distribution, the radially integrated
momentum distribution, and the angular integrated momentum
distribution explicit formulae in terms of the normal derivative
along the billiard boundary are derived.
We present a detailed numerical study
for the stadium and the cardioid billiard, which shows
in several cases that the radially integrated momentum distribution
is a good indicator of localized eigenstates,
such as scars, or bouncing ball modes.
We also find examples, where the localization
is more strongly pronounced in position space than in momentum space,
which we discuss in detail.
Finally applications and generalizations are discussed.
- Download:
- Please refer to the above published version.
(The preprint version of this article can be obtained as
Ulm report
ULM-TP/99-2
(March 1999), 30 pp.)
Illustration
The following figures show eigenstates
in position and momentum representation (3D plots)
and their grey-scale projections below.
Beneath the radially integrated angular momentum
distribution
I(φ) and for comparison
the Husimi Poincaré representation
Hn(s,p)
is shown
116th eigenstate in the cardioid billiard
567th eigenstate in the cardioid billiard
Last modified: 27 October 2004, 16:21:49
Impressum, © Arnd Bäcker
