Weak localization in disordered systems at the ballistic limit

The weak localization contribution to the two-level correlation function R(ω) is calculated for two-dimensional disordered conductors. Our analysis extends to the nondiffusive (ballistic) regime, where the elastic mean path is of order of the size of the system. In this regime, the structure factor S(t) [the Fourier transform of R(ω)] exhibits a singular behavior consisting of dips superimposed on a smooth positive background. The strongest dips appear at periods of the periodic orbits of the underlying clean system. Somewhat weaker singularities appear at times that are sums of periods of two such orbits. The results elucidate various aspects of the weak-localization physics of ballistic chaotic systems.