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, atomic clusters, etc. It is based on statistical properties of chaotic excited states which are formed by the interaction between particles. A type of “microcanonical” partition function is introduced and expressed in terms of the average shape of eigenstates ${F(E}_k,E),$ where $E$ is the total energy of the system. This partition function plays the same role as the canonical expression $\exp (-E^{\mathrm{}\left(i\right)\mathrm{}}/T)$ for open systems in a thermal bath. The approach allows one to calculate mean values and nondiagonal matrix elements of different operators. In particular, the following problems have been considered: the distribution of occupation numbers and its relevance to the canonical and Fermi-Dirac distributions; criteria of equilibrium and thermalization; the thermodynamical equation of state and the meaning of temperature, entropy and heat capacity; and the increase of effective temperature due to the interaction. The problems of spreading widths and the shape of the eigenstates are also studied.