  It was found recently that processes of multidimensional tunneling are
generally described at high energies by unstable semiclassical trajectories. We
study two observational signatures related to the instability of trajectories.
First, we find an additional power-law dependence of the tunneling probability
on the semiclassical parameter as compared to the standard case of potential
tunneling. The second signature is substantial widening of the probability
distribution over final-state quantum numbers. These effects are studied using
modified semiclassical technique which incorporates stabilization of the
tunneling trajectories. The technique is derived from first principles. We
obtain expressions for the inclusive and exclusive tunneling probabilities in
the case of unstable semiclassical trajectories. We also investigate the "phase
transition" between the cases of stable and unstable trajectories across
certain "critical" value of energy. Finally, we derive the relation between the
semiclassical probabilities of tunneling from the low-lying and highly excited
initial states. This puts on firm ground a conjecture made previously in the
semiclassical description of collision-induced tunneling in field theory.
