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Chaos experiments

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Acoustic Chaos truecm

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). truecm

C. Ellegaard, T. Guhr, K. Lindemann, H. Lorensen, J. Nygård and M. Oxborrow truecm

Experimental Observation of the Lorentz Group in Nonlinear Circuits truecm

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. truecm

(H. Svensmark) and P. Dimon



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