Acoustic Figures A. D. Jackson 7 May 2007

Ernst Florenz Friedrich Chladni ( )

Some of Chaldni’s original acoustic figures

Hans Christian Ørsted ( )

Kongens Nytorv, 4-5 September 1807

These dust piles fascinated Faraday

Sophie Germain (1776 – 1831)

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!

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

Charles Wheatstone ( )

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.

a=1a=1.2 a=100

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

“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!)

…It’s time for some acoustic coffee!