Quantum and Acoustic Chaos
We use acoustic resonators to study outstanding problems in quantum chaos. These experiments will yield a deeper understanding of the influence of the structure of the classical phase space on the wave properties. By using quartz plates, we can achieve a high quality factor for the resonator, allowing us to accurately follow the eigenvalues under a parametric perturbation. Hence, we can resolve nearly degenerate eigenvalues and obtain accurate statistics which are necessary to observe phenomena such as chaos-assisted tunneling.
The experimental setup is shown in the picture. The plate of interest is kept in a vaccum chamber. A Network Analyzer is used to generate and measure a range of frequencies from 10 Hz to 1.5 MHz. Ruby tipped transducers are used to couple weakly to the plate.
The modes of the plate correspond to the peaks in the transmission spectrum (see plot.)
Experiments
Using this experimental setup we are conducting experiments on the following issues.
- Eigenvalue statistics of mixed systems; chaos assisted tunneling. - The Clover Geometry.
- Eigenvalue statistics in spatially disordered plates.
- Level correlations in a chaotic system.
Another focus of our studies is in investigating the extent to which the universality observed in quantum chaos systems carries over to wave systems that are nonlinear. Faraday surface waves are an example of nonlinear wave systems. Scarred patterns are observed just above the primary parametric instability when a fluid with low viscosity is vibrated vertically in a stadium shaped geometry. A picture of the experimental system is shown in the Figure. A bouncing ball mode can be observed on the monitor. The stadium shaped container is located towards the bottom right of the picture.
Interesting Quantum Chaos related links:
Simulation of ray trajectories in a stadium (and circle.) Link.
Contact:
Arshad Kudrolli
akudrolli@clarku.edu
Department of Physics
Clark University
Worcester, MA 01610
