Regular structures with random interactions: A new paradigm

Abstract

Embedded random matrix ensembles opened up a new paradigm of regular structures with random interactions in isolated finite quantum systems. This is a quite a different application of embedded ensembles. Described are: (i) basic results for regular structures from random interaction in nuclear shell model and interacting boson models; (ii) regularities in ground state structure in two-level boson systems; (iii) regularities in energy centroids defined over group irreducible representations (irreps); (iv) regularities in spectral variances over group irreps with random interactions; (v) regular structures generated by EGOE(1+2)-s, EGOE(1+2)-π, BEGOE(1+2)-F and BEGOE(1+2)-S1 ensembles; (vi) correlations between diagonal Hamiltonian matrix elements and eigenvalues. These results confirm, as stated aptly by Zelevinsky and Volya that the standard textbook ideas of the factors that form the low-lying structure of a closed self-sustaining mesoscopic systems are insufficient. The quantum numbers of the ground states and some regularities of spectra emerge not necessarily due to the corresponding coherent parts of the inter-particle interaction. © 2014 Springer International Publishing Switzerland.