From Quantum Disorder to Quantum Chaos

We study the statistics of wave functions in a ballistic chaotic system. The statistical ensemble is generated by adding weak smooth random potential, which allows us to apply the ballistic (sigma) model approach. We analyze conditions of applicability of the (sigma) model, emphasizing the role played by the single particle mean free path and the Lyapunov exponent due to the random potential. In particular, we present a resolution of the puzzle of repetitions of periodic orbits counted differently by the (sigma) model and by the trace formula.