Statistics of spectra of disordered systems near the metal-insulator transition

B. I. Shklovskii, B. Shapiro, B. R. Sears, P. Lambrianides, H. B. Shore

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We study the nearest-level-spacing distribution function P(s) in a disordered system near the metal-insulator transition. We claim that in the limit of an infinite system there are only three possible functions P(s): Wigner surmise PW(s) in a metal, Poisson law PP(s) in an insulator, and a third one PT(s), exactly at the transition. The function PT is an interesting hybrid of PW(s) and PP(s), it has the small-s behavior of the former and the large-s behavior of the latter one. A scaling theory of critical behavior of P(s) in finite samples is proposed and verified numerically.

Original languageEnglish (US)
Pages (from-to)11487-11490
Number of pages4
JournalPhysical Review B
Issue number17
StatePublished - 1993


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