Periodic Orbits, Breaktime and Localization

The idea of classical action correlation is extended in order to give semiclassical explanation for the quantal dynamics of a particle in a disordered system. Starting from the semiclassical trace formula, it is commonly argued that the breaktime, which is related to the breakdown of the diagonal approximation, is determined by the Heisenberg time and hence is volume dependent. For a disordered system the breaktime may be `disorder limited' rather than `volume limited', leading to localization if it is shorter than the ergodic time. Qualitative agreement with scaling theory of localization in one to three dimensions is demonstrated