Wave function correlations on the ballistic scale: Exploring quantum chaos by quantum disorder

We study the statistics of wave functions in a ballistic chaotic system. The statistical ensemble is generated by adding weak smooth disorder. The conjecture of Gaussian fluctuations of wave functions put forward by Berry [J. Phys. A 10, 2083 (1977)] and generalized by Hortikar and Srednicki [Phys. Rev. Lett. 80, 1646 (1998); Phys. Rev. E 57, 7313 (1998)] is proven to hold on sufficiently short distances, while it is found to be strongly violated on larger scales. This also resolves the conflict between the above conjecture and the wave function normalization. The method is further used to study ballistic correlations of wave functions in a random magnetic field.