Semiclassical localization in a one-dimensional random analytic potential Journal Articles uri icon

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abstract

  • A careful semiclassical analysis of ‘‘above-barrier’’ localization is provided for the case of one-dimensional random analytic potentials. The result is a practical semiclassical formula for the localization length, which shows exponential unboundedness in the classical limit. The algebraic, ℏ→0, asymptotic series for the density of states is also determined. In the process of deriving the latter result an interesting link between the density of states and the localization length (via the Lyapunov exponent) is revealed. In addition, the results of this paper provide some of the groundwork for the semiclassical analysis of ‘‘nonadiabatic transport’’ associated with time-varying potentials.

publication date

  • November 1, 1988