Scaling near the quantum chaos border in interacting fermi systems
The emergence of quantum chaos for interacting Fermi systems is investigated by numerical calculation of the level spacing distribution P(s) as a 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=(Uepsilon(alpha)-u(0))epsilon(1/(2nu)), 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 approximately 2.0, the finiteness of nu, which comes from the increase of the Fock space size with epsilon, suggests that the transition becomes sharp as epsilon increases.