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Acoustic Figures A. D. Jackson 7 May 2007. Ernst Florenz Friedrich Chladni (1756-1827)

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Presentation on theme: "Acoustic Figures A. D. Jackson 7 May 2007. Ernst Florenz Friedrich Chladni (1756-1827)"— Presentation transcript:

1 Acoustic Figures A. D. Jackson 7 May 2007

2 Ernst Florenz Friedrich Chladni ( )

3 Some of Chaldni’s original acoustic figures

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6 Hans Christian Ørsted ( )

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8 Kongens Nytorv, 4-5 September 1807

9 These dust piles fascinated Faraday

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15 Sophie Germain (1776 – 1831)

16 Germain primes, [p,q] if p is prime and q=(2p+1) is also prime. Substantial contributions to Fermat’s last theorem. A correct description of acoustic resonances in thin plates. She received Napoleon’s prize on her 3 rd attempt. One kilo of pure gold!

17 Michael Faraday ( ) Ørsted’s dust piles inspired the discovery of electromagnetic induction.

18 Charles Wheatstone ( )

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25 Heusler, Müller, Altland, Braun, Haake, “Periodic-Orbit Theory of Level Correlations” arXiv:nlin/ “We present a semiclassical explanation of the so-called Bohigas-Giannoni-Schmidt conjecture which asserts universality of spectral fluctuations in chaotic dynamics. We work with a generating function whose semiclassical limit is determined by quadruplets of sets of periodic orbits. The asymptotic expansions of both the non-oscillatory and the oscillatory part of the universal spectral correlator are obtained. Borel summation of the series reproduces the exact correlator of random-matrix theory.” … a less general but simpler picture might be useful.

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27 a=1a=1.2 a=100

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29 Nearest-neighbor distributions for the cardioid family: spectrum of N (always RMT) spectrum of H (Poisson to RMT)

30 “Random” billiards: Nearest-neighbor distributions for random billiards: (Note that spectrum of N is always given by RMT.) Gaussian distributed (RMT for all t > 0) Poisson distributed Since spectral correlations of N are always RMT, the change in the statistics of H can only be due to the support of this spectrum. (There is nothing else!)

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32 …It’s time for some acoustic coffee!


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