Quantum Chaos Effects in Mechanical Wave Systems
Quantum chaos effects, such as wavefunction scarring and Wigner- Dyson level-spacings distributions, have been observed in a number of analogue experimental systems, including microwave cavities, water surface waves, acoustic cavities, and mechanical elastic wave systems. We describe experiments on two such mechanical wave systems, 1) elastic membranes - i.e., drumheads - which obey an underlying Helmholtz equation, and 2) thin metal plates undergoing transverse vibrations which are described by a biharmonic wave equation. For the elastic membrane system we have extensively studied the spectral statistics of both circular and stadium-shaped geometries with clamped boundary conditions; limited information about the spatial structure of high order eigenmodes has also been obtained. In plate experiments, a thin stadium-shaped plate is vibrated mechanically subject to fully clamped boundaries. High order eigenmodes are imaged using time-averaged holographic interferometry and show clear evidence of scarring. Adopting an eikonal form of the solution along classical trajectories of the stadium billiard and treating the problem exactly at the boundaries, we have obtained and experimentally verified novel quantization conditions for the observed modes.
KeywordsPeriodic Orbit Helmholtz Equation Random Matrix Theory Clamp Boundary Condition Vibrational Amplitude
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- Alt, H. et al. (1996): Phys. Rev. E 54, 2303Google Scholar
- Blümel R., Davidson I. H., Reinhardt W. P., Lin H., Sharnoff M. (1992): Phys. Rev. A 45, 2641Google Scholar
- Bogomolny E., Hughes E. (1998): Phys. Rev. E 57, 5404Google Scholar
- Chen L. H. (1996): Undergraduate thesis, Duke UniversityGoogle Scholar
- Chinnery P. A., Humphrey V. F. (1996): Phys. Rev. E 53, 272Google Scholar
- Deus S., Koch P., Sirko L. (1995): Phys. Rev. E 52, 1146Google Scholar
- Landau L. D., Lifshitz E. M. (1970): Theory of Elasticity, 2nd ed. (Pergammon, London)Google Scholar
- Starobin A. J. (1997): Undergraduate thesis, Duke UniversityGoogle Scholar
- Starobin A. J., Teitsworth S. W. (1999): submitted for publication in Phys. Rev. E Google Scholar
- Thurstone C. (1992): Undergraduate thesis, Duke UniversityGoogle Scholar
- Vest C. M. (1979): Holographic interferometry (Wiley, New York)Google Scholar