Spectral densities and partition functions of modular quantum systems as derived from a central limit theorem

Using a central limit theorem for arrays of interacting quantum systems, we give analytical expressions for the density of states and the partition function at finite temperature of such a system, which are valid in the limit of infinite number of subsystems. Even for only small numbers of subsystems we find good accordance with some known, exact results.Comment: 6 pages, 4 figures, some steps added to derivation, accepted for publication in J. Stat. Phy