Divergence of classical trajectories and weak localization

Abstract

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 ${\mathit{t}}_{\mathit{E}}$=${\lambda }^{\mathrm{-}1}$|lnħ|, where λ is the Lyapunov exponent. In the semiclassical regime ${\mathit{t}}_{\mathit{E}}$ 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. © 1996 The American Physical Society.