Spectral fluctuations of classically chaotic quantum systems

Semiclassical cross section correlations

“…Quantum systems whose classical limit is chaotic show fluctuations in cross sections and eigenvalue positions whose statistical properties seem to fall into a few universality classes [1][2][3]. Among the many measures that have been applied to characterize these statistical features, much attention has been given to two-point correlation functions since they can under certain assumptions be related to the classical dynamics [4].…”

Fano interference and cross-section fluctuations in molecular photodissociation

“…Spectral correlations of closed quantum systems, whose associated classical dynamics are chaotic, are known to be nearly universal and can be modeled by the Gaussian invariant ensembles of random matrix theory [1,2,3]. When such systems become open through their coupling to continuum channels, their bound states acquire decay widths and become resonances, but they are still expected to exhibit universal statistics [4].…”

“…The matrix H 0 is taken to be a N × N random matrix [1] from the Gaussian Orthogonal Ensemble (GOE) or from the Gaussian Unitary Ensemble (GUE), with distribution P (H 0 ) dH 0 ∝ exp[−(βN/4)TrH 2 0 ] dH 0 . Here β = 1 in the GOE and β = 2 in the GUE.…”

“…Defining C(E, t) = ∞ −∞ dω e iωt S(E, ω), and using (5) we find where b 2,β (t) is the two-level form factor [1], and A β (t), B β (t) are functions that depend in general on the matrix M in Eq. (6) and the dipole coupling coefficients to the continuum α ch c .…”

New evidence of GOE statistics for compound nuclear resonances

“…Further analyses including amplitudes [3], as well as higher than two-point correlations [4] confirmed these findings. Yet recently additional more stringent tests were proposed concerning both level statistics [5] and correlations between levels and intensities [6]. In the present article we analyse the nuclear data ensemble according to these new very sensitive tests.…”