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artículo con referato
"Decoherence as Decay of the Loschmidt Echo in Lorentz Gas"
F.M. Cucchietti, H.M. Pastawski and D.A. Wisniacki
Phys. Rev. E 65(4): Rapid Comm. (2002) 045206(R)/1-4
Classical chaotic dynamics is characterized by the exponential sensitivity to initial conditions. Quantum mechanics, however, does not show this feature. We consider instead the sensitivity of quantum evolution to perturbations in the Hamiltonian. This is observed as an attenuation of the Loschmidt Echo, M(t), i.e. the amount of the original state (wave packet of width σ) which is recovered after a time reversed evolution, in presence of a classically weak perturbation. By considering a Lorentz gas of size L, which for large L is a model for an unbounded classically chaotic system, we find numerical evidence that, if the perturbation is within a certain range, M(t) decays exponentially with a rate 1/Tφdetermined by the Lyapunov exponent λ of the corresponding classical dynamics. This exponential decay extends much beyond the Eherenfest time tE and saturates at a time ts ~ λ-1 ln[Ñ], where Ñ ~ (L/σ)2 is the effective dimensionality of the Hilbert space. Since tφ quantifies the increasing uncontrollability of the quantum phase (decoherence) its characterization and control has fundamental interest.
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