Indexed on: 15 Mar '03Published on: 15 Mar '03Published in: Physical review. E, Statistical, nonlinear, and soft matter physics
We reexamine the problem of the "Loschmidt echo," that measures the sensitivity to perturbation of quantum-chaotic dynamics. The overlap squared M(t) of two wave packets evolving under slightly different Hamiltonian is shown to have the double-exponential initial decay proportional to exp(-constant x e(2lambda(0)t)) in the main part of the phase space. The coefficient lambda(0) is the self-averaging Lyapunov exponent. The average decay (-)M proportional to e(-lambda(1)t) is single exponential with a different coefficient lambda(1). The volume of phase space that contributes to (-)M vanishes in the classical limit variant Planck-->0 for times less than the Ehrenfest time tau(E)=1/2lambda0(-1)|ln Planck|. It is only after the Ehrenfest time that the average decay is representative for a typical initial condition.