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

Abstract

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.

17 pages, 2 figures, textual improvements

References in corpus (3)

• Fidelity Decay as an Efficient Indicator of Quantum Chaos
• Echoes in classical dynamical systems
• Uniform semiclassical wave function for coherent 2D electron flow

Cited by in corpus (6)

• Semiclassical evaluation of quantum fidelity
• Signatures of many-body localisation in a system without disorder and the relation to a glass transition
• Dephasing representation: Employing the shadowing theorem to calculate quantum correlation functions
• Exact Fidelity and Full Fidelity Statistics in Regular and Chaotic Surroundings
• The quantum fidelity for the time-dependent singular quantum oscillator
• About Quantum Revivals, Quantum Fidelity, A semiclassical Approach