Statistics of random quasi 1D Hamiltonian with slowly varying parameters. Painlev\'{e} again.

P. G. Silvestrov

doi:10.1016/0375-9601(95)00834-6

Statistics of random quasi 1D Hamiltonian with slowly varying parameters. Painlev\'{e} again.

Condensed Matter 2016-08-31 v1 chao-dyn High Energy Physics - Theory Chaotic Dynamics

Authors: P. G. Silvestrov

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Abstract

The statistics of random band--matrices with width and strength of the band slowly varying along the diagonal is considered. The Dyson equation for the averaged Green function close to the edge of spectrum is reduced to the Painlev\'{e} I equation. The analytical properties of the Green function allow to fix the solution of this equation. The former appears to be the same as that arose within the random--matrix regularization of 2d-gravity.

Keywords

random band matrices Dyson equation Painlevé I equation Green's function spectrum edge 2d gravity

Cite

@article{arxiv.cond-mat/9503077,
  title  = {Statistics of random quasi 1D Hamiltonian with slowly varying parameters. Painlev\'{e} again.},
  author = {P. G. Silvestrov},
  journal= {arXiv preprint arXiv:cond-mat/9503077},
  year   = {2016}
}

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9 pages, latex, no figures.

Statistics of random quasi 1D Hamiltonian with slowly varying parameters. Painlev\'{e} again.

Abstract

Keywords

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