Chaos Thresholds in finite Fermi systems

TL;DR

This paper investigates the onset of quantum chaos in finite Fermi systems, showing that a transition in energy level statistics can occur even below the direct interaction threshold due to high-order interactions.

Contribution

It introduces a new scheme to analyze the transition to quantum chaos, emphasizing the role of high-order interactions and the factorial divergence of Feynman diagrams.

Findings

Transition from Poisson to Wigner-Dyson statistics can occur below the interaction threshold.

The change in energy level statistics resembles a narrow phase transition.

High-order interactions govern the quantum chaos development in finite Fermi systems.

Abstract

The development of Quantum Chaos in finite interacting Fermi systems is considered. At sufficiently high excitation energy the direct two-particle interaction may mix into an eigen-state the exponentially large number of simple Slater-determinant states. Nevertheless, the transition from Poisson to Wigner-Dyson statistics of energy levels is governed by the effective high order interaction between states very distant in the Fock space. The concrete form of the transition depends on the way one chooses to work out the problem of factorial divergency of the number of Feynman diagrams. In the proposed scheme the change of statistics has a form of narrow phase transition and may happen even below the direct interaction threshold.