The survival probability and the local density of states for one-dimensional Hamiltonian systems

Details The survival probability and the local density of states for one-dimensional Hamiltonian systems The survival probability and the local density of states for one-dimensional Hamiltonian systems

2003-03-17

arxiv.org/abs/quant-ph/0303103v2

J. Phys. A: Math. Gen. 36, 9591 (2003).

Physics

Quantum Physics

17 pages, 2 figures, textual improvements

Scientific paper

10.1088/0305-4470/36/36/310

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.

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