Higher-order level spacings in random matrix theory based on Wigner's conjecture

2020/05/31 by Wen-Jia Rao · 1 citation
Physics and Astronomy · #cond-mat.dis-nn

paper · pdf · doi:10.1103/physrevb.102.054202

published as Phys. Rev. B 102, 054202 (2020) · 7 pages, 4 figures

arxiv created 2020/08/04 · arxiv updated 2020/08/05

Abstract

The distribution of higher order level spacings, i.e. the distribution of \s_i⁽ⁿ⁾=E_i+n-E_i\ with n≥ 1 is derived analytically using a Wigner-like surmise for Gaussian ensembles of random matrix as well as Poisson ensemble. It is found s⁽ⁿ⁾ in Gaussian ensembles follows a generalized Wigner-Dyson distribution with rescaled parameter α=νC_n+1²+n-1, while that in Poisson ensemble follows a generalized semi-Poisson distribution with index n. Numerical evidences are provided through simulations of random spin systems as well as non-trivial zeros of Riemann zeta function. The higher order generalizations of gap ratios are also discussed.

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