Convergence of moment expansions for expectation values with embedded random matrix ensembles and quantum chaos

Abstract

Smoothed forms for expectation values 〈 K 〉 E of positive definite operators K follow from the K-density moments either directly or in many other ways each giving a series expansion (involving polynomials in E). In large spectroscopic spaces one has to partition the many particle spaces into subspaces. Partitioning leads to new expansions for expectation values. It is shown that all the expansions converge to compact forms depending on the nature of the operator K and the operation of embedded random matrix ensembles and quantum chaos in many particle spaces. Explicit results are given for occupancies 〈 n i 〉 E , spin-cutoff factors 〈 J Z 2〉 E and strength sums 〈 O † O〉 E , where O is a one-body transition operator.