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Regular Structures with Random Interactions: A New Paradigm

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Embedded Random Matrix Ensembles in Quantum Physics

Part of the book series: Lecture Notes in Physics ((LNP,volume 884))

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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.

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  1. Physical Research Laboratory, Ahmedabad, India

    V. K. B. Kota

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Kota, V.K.B. (2014). Regular Structures with Random Interactions: A New Paradigm. In: Embedded Random Matrix Ensembles in Quantum Physics. Lecture Notes in Physics, vol 884. Springer, Cham. https://doi.org/10.1007/978-3-319-04567-2_14

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