  We address the time decay of the Loschmidt echo, measuring sensitivity of
quantum dynamics to small Hamiltonian perturbations, in one-dimensional
integrable systems. Using semiclassical analysis, we show that the Loschmidt
echo may exhibit a well-pronounced regime of exponential decay, alike the one
typically observed in quantum systems whose dynamics is chaotic in the
classical limit. We derive an explicit formula for the exponential decay rate
in terms of the spectral properties of the unperturbed and perturbed Hamilton
operators and the initial state. In particular, we show that the decay rate,
unlike in the case of the chaotic dynamics, is directly proportional to the
strength of the Hamiltonian perturbation. Finally, we compare our analytical
predictions against the results of a numerical computation of the Loschmidt
echo for a quantum particle moving inside a one-dimensional box with
Dirichlet-Robin boundary conditions, and find the two in good agreement.
