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The survival probability and the local density of states for one-dimensional Hamiltonian systems
For chaotic systems there is a theory for the decay of the survival
probability, and for the parametric dependence of the local density of states.
This theory leads to the distinction between "perturbative" and
"non-perturbative" regimes, and to the observation that semiclassical tools are
useful in the latter case. We discuss what is "left" from this theory in the
case of one-dimensional systems. We demonstrate that the remarkably accurate
{\em uniform} semiclassical approximation captures the physics of {\em all} the
different regimes, though it cannot take into account the effect of strong
localization.Comment: 17 pages, 2 figures, textual improvement