Universal statistics of wave functions in chaotic and disordered systems
  We study a new statistics of wave functions in several chaotic and disordered systems: the random matrix model, band random matrix model, the Lipkin model, chaotic quantum billiard and the 1D tight-binding model. Both numerical and analytical results show that the distribution function of a generalized Riccati variable, defined as the ratio of components of eigenfunctions on basis states coupled by perturbation, is universal, and has the form of Lorentzian distribution. 
Bambi Hu, Baowen Li, and Weng-ge Wang (Department of Physics and   Center for Nonlinear Studies, Hong Kong Baptist Universit...