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Spectral correlations in systems undergoing a transition from periodicity to disorder

T. Dittrich·B. Mehlig·H. Schanz·Uzy Smilansky·Peter Pollner·Gabor Vattay
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Abstract

We study the spectral statistics for extended yet finite quasi 1-d systems which undergo a transition from periodicity to disorder. In particular we compute the spectral two-point form factor, and the resulting expression depends on the degree of disorder. It interpolates smoothly between the two extreme limits -- the approach to Poissonian statistics in the (weakly) disordered case, and the universal expressions derived for the periodic case. The theoretical results agree very well with the spectral statistics obtained numerically for chains of chaotic billiards and graphs.

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T. Dittrich, B. Mehlig, H. Schanz, Uzy Smilansky, Peter Pollner, Gabor Vattay. 1998-11-23. Spectral correlations in systems undergoing a transition from periodicity to disorder. https://doi.org/10.1103/physreve.59.6541

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