  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.
