Quantum Chaos Effects in Mechanical Wave Systems

  • Stephen W. Teitsworth
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 547)


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.


Periodic Orbit Helmholtz Equation Random Matrix Theory Clamp Boundary Condition Vibrational Amplitude 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Stephen W. Teitsworth
    • 1
  1. 1.Department of PhysicsDuke UniversityDurhamUSA

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