About Quantum Revivals, Quantum Fidelity, A semiclassical Approach

Abstract

In this paper we develop the topics of Quantum Recurrences and of Quantum Fidelity which have attracted great interest in recent years. The return probability is given by the square modulus of the overlap between a given initial wavepacket and the corresponding evolved one; quantum recurrences in time can be observed if this overlap is unity. We provide some conditions under which this is semiclassically achieved taking as initial wavepacket a coherent state located on a closed orbit of the corresponding classical motion. The "quantum fidelity" (or Loschmidt Echo) is the square modulus of the overlap of an evoloved quantum state with the same evoloved by a slightly perturbed Hamiltonian. Its decrease in time measures the sensitivity of Quantum Evolution with respect to small perturbations. It is believed to have significantly different behavior in time when the underlying classical motion is chaotic or regular. Starting with suitable initial quantum states, we develop a semiclassical estimate of this quantum fidelity in the Linear Response framework (appropriate for the small perturbation regime), assuming some ergodicity conditions on the corresponding classical motion.

References in corpus (11)

• Quantum wave packet revivals
• Decoherence and the Loschmidt echo
• A random matrix formulation of fidelity decay
• Universality of the Lyapunov regime for the Loschmidt echo
• Noiseless scattering states in a chaotic cavity
• Stability of Quantum Motion: Beyond Fermi-golden-rule and Lyapunov decay
• Anomalous power law of quantum reversibility for classically regular dynamics
• Faster than Lyapunov decays of classical Loshcmidt echo
• On the stability of classical chaotic motion under system's perturbations
• Recurrence of fidelity in near integrable systems
• Fidelity Decay Saturation Level for Initial Eigenstates

Cited by in corpus (5)

• Quantum Chaos and Thermalization in Isolated Systems of Interacting Particles
• Decoherence, Entanglement and Irreversibility in Quantum Dynamical Systems with Few Degrees of Freedom
• Stability of quantum motion in regular systems: a uniform semiclassical approach
• Stability of Fock states in a two-component Bose-Einstein condensate with a regular classical counterpart
• Sensitivity of Quantum Motion to Perturbation in Triangle Map