2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/98678We 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 $σ$-model approach. We analyze conditions of applicability of the $σ$-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 $σ$-model and by the trace formula.15 pages, no figures. Contribution to a special issue of J. Low Temp. Phys. dedicated to Peter Woelfle's 60th birthdayMesoscale and Nanoscale PhysicsChaotic Dynamicstext