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.