STATISTICAL-THEORY OF FINITE FERMI SYSTEMS BASED ON THE STRUCTURE OF CHAOTIC EIGENSTATES

An approach is developed for the description of isolated Fermi systems with finite numbers of particles, such as complex atoms, nuclei, atom ic clusters, etc. It is based on statistical properties of chaotic exc ited states which are formed by the interaction between particles. A t ype of ''microcanonical'' partition function is introduced and express ed in terms of the average shape of eigenstates F(E-k,E), where E is t he total energy of the system. This partition function plays the same role as the canonical expression exp(-E-(i)/T) for open systems in a t hermal bath. The approach allows one to calculate mean values and nond iagonal matrix elements of different operators. In particular, the fol lowing problems have been considered: the distribution of occupation n umbers and its relevance to the canonical and Fermi-Dirac distribution s; criteria of equilibrium and thermalization; the thermodynamical equ ation of state and the meaning of temperature, entropy and heat capaci ty; and the increase of effective temperature due to the interaction. The problems of spreading widths and the shape of the eigenstates art also studied.