Embedded GOE ensembles for interacting boson systems: BEGOE(1+2) for spinless bosons

Abstract

Embedded GOE generated by random two-body interactions in the presence of a one-body mean-field for spinless boson systems is introduced [it is called BEGOE(1+2) with 'B' for bosons] and a method for its construction is given. Using unitary decomposition and trace propagation, formulas for the lowest four moments of the eigenvalue density generated by a general one plus two-body interaction are obtained. These are used to show that in the dense limit, the eigenvalue density for BEGOE(1+2) will approach Gaussian form and for strong enough two-body interaction there is average fluctuation separation. In addition, using numerical calculations, it is shown that BEGOE(1+2) admits three transition (or chaos) markers just as EGOE(1+2) and EGOE(1+2)-s. © 2014 Springer International Publishing Switzerland.