Golden rule decay versus Lyapunov decay of the quantum Loschmidt echo

Details Golden rule decay versus Lyapunov decay of the quantum Loschmidt echo Golden rule decay versus Lyapunov decay of the quantum Loschmidt echo

2001-07-19

arxiv.org/abs/nlin/0107044v2

Phys. Rev. E 64, 055203(R) (2001).

Nonlinear Sciences

Chaotic Dynamics

4 pages, 4 .eps figures

Scientific paper

10.1103/PhysRevE.64.055203

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

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