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 (1791-1867) Ørsted’s dust piles inspired the discovery of electromagnetic induction.
Heusler, Müller, Altland, Braun, Haake, “Periodic-Orbit Theory of Level Correlations” arXiv:nlin/0610053 “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.
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!)
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