Scaling near Quantum Chaos Border in Interacting Fermi Systems

Details Scaling near Quantum Chaos Border in Interacting Fermi Systems Scaling near Quantum Chaos Border in Interacting Fermi Systems

2000-04-14

arxiv.org/abs/cond-mat/0004237v2

Physics

Condensed Matter

Strongly Correlated Electrons

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

Scientific paper

10.1103/PhysRevE.62.R7575

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.

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