Stability of quantum motion in regular systems: a uniform semiclassical approach

Abstract

We study the stability of quantum motion of classically regular systems in presence of small perturbations. Onthe base of a uniform semiclassical theory we derive the fidelity decay which displays a quite complexbehaviour, from Gaussian to power law decay $t^{-\alpha }$ with $1\le \alpha \le 2$. Semiclassical estimates are given for the time scales separating the different decaying regions and numerical results are presented which confirm our theoretical predictions.

5 pages, 4 figures, published version

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Cited by in corpus (10)

• Loschmidt Echo
• Decoherence, Entanglement and Irreversibility in Quantum Dynamical Systems with Few Degrees of Freedom
• An initial value representation for the Loschmidt echo
• Semiclassical Approach to Survival Probability at Quantum Phase Transitions
• Complexity and instability of quantum motion near a quantum phase transition
• Scaling behavior for a class of quantum phase transitions
• On the origin of the exponential decay of the Loschmidt echo in integrable systems
• Stability of Fock states in a two-component Bose-Einstein condensate with a regular classical counterpart
• Semiclassical approach to the quantum Loschmidt echo in deep quantum regions: from validity to breakdown
• Sensitivity of Quantum Motion to Perturbation in Triangle Map