Divergence of classical trajectories and weak localization

We study the weak-localization correction (WLC) to transport coefficients of a system of electrons in a static long-range potential (e.g., an antidot array or ballistic cavity). We found that the weak-localization correction to the current response is delayed by the large time t(E)=lambda(-1)/Inh/, where lambda is the Lyapunov exponent. In the semiclassical regime t(E) is much larger than the transport lifetime. Thus, the fundamental characteristic of the classical chaotic motion, Lyapunov exponent, may be found by measuring the frequency or temperature dependence of WLC.