Spectral correlations in systems undergoing a transition from periodicity to disorder

T. Dittrich, B. Mehlig, H. Schanz, Uzy Smilansky, Péter Pollner, Gábor Vattay

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Abstract

We study the spectral statistics for extended yet finite quasi-one-dimensional 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 in T. Dittrich, B. Mehlig, H. Schanz, and U. Smilansky, Chaos Solitons Fractals 8, 1205 (1997); Phys. Rev. E 57, 359 (1998); B. D. Simons and B. L. Altshuler, Phys. Rev. Lett. 70, 4063 (1993); and N. Taniguchi and B. L. Altshuler, ibid. 71, 4031 (1993) for the periodic case. The theoretical results agree very well with the spectral statistics obtained numerically for chains of chaotic billiards and graphs.

Original languageEnglish
Pages (from-to)6541-6551
Number of pages11
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume59
Issue number6
DOIs
Publication statusPublished - Jan 1 1999

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ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Physics and Astronomy(all)

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