The Wigner distribution and 2D classical maps
arXiv:1407.1949 · doi:10.1016/j.physleta.2017.05.008
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.
Low-resolution figures (as before); non-generic example added; higher-order spacings briefly discussed
References in corpus (7)
- Semiclassical Foundation of Universality in Quantum Chaos
- Periodic-Orbit Theory of Level Correlations
- Leading off-diagonal approximation for the spectral form factor for uniformly hyperbolic systems
- Periodic-orbit theory of universal level correlations in quantum chaos
- Stickiness in Hamiltonian systems: from sharply divided to hierarchical phase space
- Resummation and the semiclassical theory of spectral statistics
- Nearest-neigbor spacing distributions of the beta-Hermite ensemble of random matrices