Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2009-11-24
Sa\'ul Hern\'andez-Quiroz and Luis Benet, Phys. Rev. E 81, 036218 (2010) [12 pages]
Nonlinear Sciences
Chaotic Dynamics
13 pages (double column), 7 figures some in color. The movies can be obtained at http://link.aps.org/supplemental/10.1103/Phys
Scientific paper
10.1103/PhysRevE.81.036218
We study the nearest-neighbor distributions of the $k$-body embedded ensembles of random matrices for $n$ bosons distributed over two-degenerate single-particle states. This ensemble, as a function of $k$, displays a transition from harmonic oscillator behavior ($k=1$) to random matrix type behavior ($k=n$). We show that a large and robust quasi-degeneracy is present for a wide interval of values of $k$ when the ensemble is time-reversal invariant. These quasi-degenerate levels are Shnirelman doublets which appear due to the integrability and time-reversal invariance of the underlying classical systems. We present results related to the frequency in the spectrum of these degenerate levels in terms of $k$, and discuss the statistical properties of the splittings of these doublets.
Benet Luis
Hernández-Quiroz Saul
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