Golden rule decay versus Lyapunov decay of the quantum Loschmidt echo - art. no. 055203

The overlap of two wave packets evolving in time with slightly different Ha miltonians decays exponentially (proportional to)e(-gammat), for perturbati on strengths U greater than the level spacing Delta. We present numerical e vidence for a dynamical system that the decay rate gamma is given by the sm allest of the Lyapunov exponent lambda of the classical chaotic dynamics an d the level broadening U-2/Delta that follows from the golden rule of quant um mechanics. This implies the range of validity U>root lambda Delta for th e perturbation-strength independent decay rate discovered by Jalabert and P astawski [Phys. Rev. Lett. 86, 2490 (2001)].