Divergence of the 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 $t_E={\lambda }^{-1}|\ln \hslash |$, 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.

23 pages, 4 .eps figures; Major revisions in Secs. 3, 4, and 6; To appear in Phys. Rev. B, Nov. 15, 1996

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