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Wigner spacing distribution in classical mechanics

Authors
  • Sakhr, Jamal
Type
Preprint
Publication Date
Jul 09, 2014
Submission Date
Jul 08, 2014
Identifiers
arXiv ID: 1407.1949
Source
arXiv
License
Yellow
External links

Abstract

The Wigner spacing distribution has a long and illustrious history in nuclear physics and in the quantum mechanics of classically chaotic systems. In this paper, a long-overlooked connection between the Wigner distribution and classical chaos in two-degree-of-freedom (2D) conservative systems is introduced. In the specific context of fully chaotic 2D systems, the hypothesis that typical pseudotrajectories of a canonical Poincar\'{e} map have a Wignerian nearest-neighbor spacing distribution (NNSD), is put forward and tested. Employing the 2D circular stadium billiard as a generic test case, the NNSD of a typical pseudotrajectory of the Birkhoff map is shown to be in excellent agreement with the Wigner distribution. The relevance of the higher-order Wigner surmises from random matrix theory are also illustrated.

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