The Wigner distribution and 2D classical maps

TL;DR

This paper introduces a new connection between the Wigner distribution and 2D classical maps, showing that pseudo-trajectories in ergodic systems typically follow a Wignerian spacing distribution, regardless of certain system properties.

Contribution

It proposes and numerically tests the hypothesis that 2D ergodic map trajectories exhibit Wignerian spacing distributions, expanding the understanding of classical-quantum analogies.

Findings

Wigner distribution applies to 2D classical map spacings

Hypothesis holds across various system properties

Distribution robustness against mixing, symmetry, and dissipation

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 novel connection between the Wigner distribution and 2D classical mechanics is introduced. The hypothesis that typical pseudo-trajectories of a 2D ergodic map have a Wignerian nearest-neighbor spacing distribution is put forward and numerically tested. The standard Euclidean metric is used to compute the interpoint spacings. In all test cases, the hypothesis is upheld, and the range of validity of the hypothesis appears to be robust in the sense that it is not affected by the presence or absence of: (i) mixing; (ii) time-reversal symmetry; and/or (iii) dissipation.