Decay of the Loschmidt Echo for quantum states with sub-Planck scale structures

Details Decay of the Loschmidt Echo for quantum states with sub-Planck scale structures Decay of the Loschmidt Echo for quantum states with sub-Planck scale structures

2002-03-26

arxiv.org/abs/nlin/0203052v2

Phys.Rev.Lett. 89, 154103 (2002)

Nonlinear Sciences

Chaotic Dynamics

4 pages, 2 figures; accepted for publication in Physical Review Letters

Scientific paper

10.1103/PhysRevLett.89.154103

Quantum states extended over a large volume in phase space have oscillations from quantum interferences in their Wigner distribution on scales smaller than $\hbar$ [W.H. Zurek, Nature {\bf 412}, 712 (2001)]. We investigate the influence of those sub-Planck scale structures on the sensitivity to an external perturbation of the state's time evolution. While we do find an accelerated decay of the Loschmidt Echo for an extended state in comparison to a localized wavepacket, the acceleration is described entirely by the classical Lyapunov exponent and hence cannot originate from quantum interference.

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