Phys. Rev. E 64, 055203(R) (2001) [4 pages]

Golden rule decay versus Lyapunov decay of the quantum Loschmidt echo

Abstract

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Ph. Jacquod¹, P.G. Silvestrov^1,2, and C.W.J. Beenakker¹
¹Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands
²Budker Institute of Nuclear Physics, 630090 Novosibirsk, Russia

Received 19 July 2001; published 15 October 2001

The overlap of two wave packets evolving in time with slightly different Hamiltonians decays exponentially ∝e^-γt, for perturbation strengths U greater than the level spacing Δ. We present numerical evidence for a dynamical system that the decay rate γ is given by the smallest of the Lyapunov exponent λ of the classical chaotic dynamics and the level broadening U²/Δ that follows from the golden rule of quantum mechanics. This implies the range of validity U>√λΔ for the perturbation-strength independent decay rate discovered by Jalabert and Pastawski [Phys. Rev. Lett. 86, 2490 (2001)].

URL:

http://link.aps.org/doi/10.1103/PhysRevE.64.055203

DOI:

10.1103/PhysRevE.64.055203

PACS:

05.45.Mt, 05.45.Pq, 42.50.Md, 76.60.Lz

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Phys. Rev. E 64, 055203(R) (2001) [4 pages]

Golden rule decay versus Lyapunov decay of the quantum Loschmidt echo