  The Quantum Loschmidt Echo is a measurement of the sensitivity of a quantum
system to perturbations of the Hamiltonian. In the case of the standard
2-torus, we derive some explicit formulae for this quantity in the transition
regime where it is expected to decay in the semiclassical limit. The expression
involves both a two-microlocal defect measure of the initial data and the form
of the perturbation. As an application, we exhibit a non-concentration
criterium on the sequence of initial data under which one does not observe a
macroscopic decay of the Quantum Loschmidt Echo. We also apply our results to
several examples of physically relevant initial data such as coherent states
and plane waves.
