Symmetries, Self Correlations and Cross Correlations in Embedded Ensembles

Abstract

Correlations between levels with different quantum numbers generated by embedded ensembles (EEs) are very important as these “cross correlations” are absent in the description of levels of interacting particle systems if we use classical GOE or GUE or GSE ensembles. In the description using classical ensembles, one assumes independent GOE or GUE or GSE description for levels with different quantum numbers. Self correlations, i.e. correlations between levels with same quantum numbers, are also important for EEs as they will give for example information on fluctuations in energy centroids and spectral variances. Results are presented for the correlations between matrix structure, symmetries and self and cross correlations in embedded ensembles using several fermionic and bosonic embedded ensembles described in the previous chapters. It is important to emphasize that “cross correlations” is one of the very important new aspect of EEs.