Integrability, Chaos and Disorder in Wavefunctions
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.