Golden rule decay versus Lyapunov decay of the quantum Loschmidt echo

The overlap of two wave packets evolving in time with slightly different Hamiltonians decays exponentially approximate to e(-gammat), for perturbation strengths U greater than the level spacing Delta. We present numerical evidence for a dynamical system that the decay rate gamma is given by the smal...

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Published in:Physical review. E, Statistical, nonlinear, and soft matter physics Statistical, nonlinear, and soft matter physics, 2001-11, Vol.64 (5 Pt 2), p.055203-055203
Main Authors: Jacquod, P, Silvestrov, P G, Beenakker, C W
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creator Jacquod, P
Silvestrov, P G
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description The overlap of two wave packets evolving in time with slightly different Hamiltonians decays exponentially approximate to e(-gammat), for perturbation strengths U greater than the level spacing Delta. We present numerical evidence for a dynamical system that the decay rate gamma is given by the smallest of the Lyapunov exponent lambda of the classical chaotic dynamics and the level broadening U(2)/Delta that follows from the golden rule of quantum mechanics. This implies the range of validity U > the square root of [lambdaDelta] for the perturbation-strength independent decay rate discovered by Jalabert and Pastawski [Phys. Rev. Lett. 86, 2490 (2001)].
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title Golden rule decay versus Lyapunov decay of the quantum Loschmidt echo
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