Statistical Theory of Finite Fermi-Systems Based on the Structure of Chaotic Eigenstates

TL;DR

This paper develops a statistical framework for finite Fermi-systems based on chaotic eigenstates, introducing a new microcanonical partition function to analyze thermodynamic properties and eigenstate structures.

Contribution

It introduces a novel microcanonical partition function based on eigenstate shapes, enabling analysis of thermodynamics and eigenstate properties in finite Fermi-systems.

Findings

Distribution of occupation numbers aligns with Fermi-Dirac statistics.

Criteria for equilibrium and thermalization are established.

Effective temperature increases due to particle interactions.

Abstract

The approach is developed for the description of isolated Fermi-systems with finite number 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. New 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 $exp(-E^{(i)}/T)$ for open systems in thermal bath. The approach allows to calculate mean values and non-diagonal matrix elements of different operators. In particular, the following problems have been considered: distribution of occupation numbers and its relevance to the canonical and Fermi-Dirac distributions; criteria of equilibrium and thermalization; thermodynamical equation of state and the meaning of temperature, entropy and heat capacity, increase of effective temperature due to the interaction. The problems of spreading widths and shape of the eigenstates are also studied.