Sensitivity of quantum motion to perturbation in a triangle map.

We study quantum Loschmidt echo, or fidelity, in the triangle map whose classical counterpart has linear instability and weak chaos. Numerically, three regimes of fidelity decay have been found with respect to the perturbation strength epsilon. In the regime of weak perturbation, the fidelity decays as exp(-c epsilon(2)t(gamma)) with gamma approximately 1.7. In the regime of strong perturbation, the fidelity is approximately a function of epsilont(2.5), which is predicted for the classical fidelity [G. Casati, Phys. Rev. Lett. 94, 114101 (2005)], and decays slower than power-law decay for long times. In an intermediate regime, the fidelity has approximately an exponential decay exp(-c' epsilont).