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Acoustic Chaos
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Elastic bodies can be used to study the signatures of classical chaos in
wave mechanics. We have been exploring the relationship between an elastic
body's shape and the frequencies at which the body resonates. Our work
addresses the following two questions: To what extent is the shape of an
elastic body reflected in its resonance frequencies? What can be deduced
about the body's shape solely from them? The elastic bodies used in our
experiments are variously shaped blocks of aluminium and quartz. Each
block resonates at many different frequencies, whose positions in frequency
space depend in a non-trivial way on the block's shape. According to
Random Matrix Theory, however, the statistics of the spacings between these
frequencies ought to obey a ``universal'' distribution: blocks with
``regular'' shapes should exhibit Poisson statistics, whereas those having
``chaotic'' shapes should exhibit G.O.E. statistics. We have been testing
these predictions experimentally. By identifying the so-called
periodic orbits within our blocks, we in addition hope to forge a
link between experimental acoustics and the formal machinery of chaos
theory (vis. Gutzwiller's trace formula, periodic orbit theory).
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C. Ellegaard, T. Guhr, K. Lindemann, H. Lorensen, J. Nygård
and M. Oxborrow
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Experimental Observation of the Lorentz Group in Nonlinear Circuits
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We have measured Berry's geometrical phase of the Lorentz group in a pair
of connected driven dissipative electronic oscillators in the vicinity
of a period-doubling bifurcation. Surprisingly, under certain
conditions, a small signal transforms just as the Lorentz transformation
of a spinor, apart from some factors. By measuring along what
corresponds to a closed loop on a hyperboloid (the invariant surface of the
Lorentz group), we can determine Berry's phase of the Lorentz group.
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(H. Svensmark) and P. Dimon
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Mon Mar 6 19:42:06 MET 1995