Scaling near Quantum Chaos Border in Interacting Fermi Systems

Abstract

The emergence of quantum chaos for interacting Fermi systems is investigated by numerical calculation of the level spacing distribution $P(s)$ as function of interaction strength $U$ and the excitation energy $\epsilon$ above the Fermi level. As $U$ increases, $P(s)$ undergoes a transition from Poissonian (nonchaotic) to Wigner-Dyson (chaotic) statistics and the transition is described by a single scaling parameter given by $Z=(U{\epsilon }^{\alpha }-u_0){\epsilon }^{1/2\nu }$, where $u_0$ is a constant. While the exponent $\alpha$, which determines the global change of the chaos border, is indecisive within a broad range of $0.9\sim 2.0$, finite value of $\nu$, which comes from the increase of the Fock space size with $\epsilon$, suggests that the transition becomes sharp as $\epsilon$ increases.

4 pages, 4 figures, to appear in Phys. Rev. E (Rapid Communication)