Wavefunctions

Disordered Billiard:
SC2,
SC4,
SC5

Sinai Billiard

Chaotic Geometries

A unique feature of our experiments is the ability
to directly measure eigenfunctions, i.e. the spatial distribution of the waves, in
essentially arbitrary geometries. The wavefunctions are obtained using a cavity
perturbation technique developed by Sridhar. In this technique, a small metal bead
is introduced inside the cavity. If the bead is sufficiently small compared to the
wavelength, the resultant shift in frequency due to the perturbation is
proportional to the square of the Electric field (hence the wavefunction), at the
location of the bead. By moving the bead with a magnet, the wavefunction can be
mapped out. Some of the issues addressed in these experiments are:

- Scars which were predicted by Heller in 1983 were first observed by us in 1991, Phys. Rev. Lett. , 67, 785 (1991)
- Observation of Porter-Thomas distribution and fluctuations in eigenfunctions of chaotic billiards, Phys. Rev. Lett., 75, 822 (1995)
- Experimental studies of correlations of chaotic and disordered eigenfunctions and comparison with supersymmetry nonlinear sigma models, Phys. Rev. Lett., 85, 2360 (2000)

The role of chaos and impurity scattering is strikingly evident
in this summary picture below. The chaotic geometry shows essentially a
"random" distribution of the wavefunction density, with a finite probability of
large intensities, in contrast to the rectangle, where intensity distribution is
"smoother". Indeed we have shown that the denisty distribution in the chaotic
geometry obeys the Porter-Thomas law. Upon introduction of impurities in the
disordered billiards, we see a new effect, localization.