2014
DOI: 10.1209/0295-5075/107/50004
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GSE statistics without spin

Abstract: Energy levels statistics following the Gaussian Symplectic Ensemble (GSE) of Random Matrix Theory have been predicted theoretically and observed numerically in numerous quantum chaotic systems. However in all these systems there has been one unifying feature: the combination of halfinteger spin and time-reversal invariance. Here we provide an alternative mechanism for obtaining GSE statistics that is based on geometric symmetries of a quantum system which alleviates the need for spin. As an example, we constru… Show more

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Cited by 23 publications
(26 citation statements)
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“…The scattering matrix S relates the incoming amplitudes a ij with the outgoing ones b ij via b = Sa (5) arXiv:1708.06236v1 [quant-ph] 16 Aug 2017 (Color online) (a) Sketch of the graph proposed in Ref. 13 to study GSE statistics without spin. The four arrows denote bonds along which additional phases are acquired.…”
Section: A Graphs Showing Kramer's Degeneracymentioning
confidence: 99%
See 1 more Smart Citation
“…The scattering matrix S relates the incoming amplitudes a ij with the outgoing ones b ij via b = Sa (5) arXiv:1708.06236v1 [quant-ph] 16 Aug 2017 (Color online) (a) Sketch of the graph proposed in Ref. 13 to study GSE statistics without spin. The four arrows denote bonds along which additional phases are acquired.…”
Section: A Graphs Showing Kramer's Degeneracymentioning
confidence: 99%
“…The solutions of the determinant condition (9) generate the spectrum of the graph. To realize graphs with GSE symmetry Joyner et al [13] proposed the graph shown in Fig. 1.…”
Section: A Graphs Showing Kramer's Degeneracymentioning
confidence: 99%
“…1(top) was proposed in Ref. [21]. It contains two geometrically identical subgraphs but with phase shifts by +π/2 and −π/2, respectively, along two corresponding bonds.…”
mentioning
confidence: 99%
“…where a variance of one for a has been assumed. With (23) the distribution of the non-trivial eigenvalues is given by a χ distribution with f = 2 degrees of freedom. For the chiral unitary case, a and b are complex Gaussian variables and the distribution has f = 4 degrees of freedom.…”
Section: Ensemble Averaged Densitymentioning
confidence: 99%
“…3.2 of [20]). For the Gaussian unitary ensemble the number of realizations is still small, the first of them being performed in microwave billiard systems [21,22] and later in microwave networks [23]. The Gaussian symplectic ensemble usually is associated with spin 1/2 systems, but Joyner et al [24] proposed an alternative way to realize the necessary condition T 2 = −1 in a graph with a peculiarly designed geometry.…”
Section: Introductionmentioning
confidence: 99%