Sensitivity of the Loschmidt Echo as a monitor of dynamical Quantum Chaos

FERNANDO M. CUCCHIETTI; H. M. PASTAWSKI; D. A. WISNIACKI

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

The American Physical Society

Año: 2001 vol. 65 p. 45206 - 45206

1063-651X

Sensitivity of the Loschmidt Echo as a monitor of dynamical Quantum Chaos F.M. Cucchietti, H.M. Pastawski and D. Wisniacki Phys. Rev.E. 65, 045206R (2001)Abstract: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 exponential atenuation of the amount of the original state which is recovered after a perturbed time reverted evolution i.e. the Loschmidt Echo. By considering a disordered Sinai billiard, we find numerical evidence that this decay rate 1/τ is given by the Lyapunov exponent of the corresponding lassical dynamics. Thefore, the attenuation rate of the Loschmidt Echo enables a dynamical definition of quantum chaos.