Decoherence as decay of the Loschmidt echo in a Lorentz gas

F. CUCCHIETTI, H. PASTAWSKI AND D. A. WISNIACKI

PHYSICAL REVIEW E - STATISTICAL PHYSICS, PLASMAS, FLUIDS AND RELATED INTERDISCIPLINARY TOPICS

American Physical Society

Año: 2002 vol. 65 p. 452061 - 452064

1063-651X

Classical chaotic dynamics is characterized by exponential sensitivity to initial conditions. Quantum me- chanics, 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 ) which is recovered after a time reversed evolution, in the 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/determined by the Lyapunov exponent of the corresponding classical dynamics. This exponential decay extends much beyond the Eherenfest time t E and saturates at a time t s 􏱤 􏰻 1 lnN˜ , where N˜ 􏱤 ( L /) 2 is the effective dimensionality of the Hilbert space. Since quantifies the increasing uncontrollability of the quantum phase decoherence its characterization and control has fundamental interest.