Chaotic dynamics of a nonlinear oscillator is considered in the semiclassical approximation. The Loschmidt echo as a measure of quantum stability to a time dependent variation is calculated. It is shown that an exponential decay of the Loschmidt echo is due to a Lyapunov exponent and it has a pure classical nature. The Lyapunov regime is observed for a time scale which is of the power law in semiclassical parameter.

• Received 7 October 2003

DOI:https://doi.org/10.1103/PhysRevE.70.026206