ON THE HIGH-ENERGY SUPPRESSION OF TRANSITION AMPLITUDES IN THE DRIVENANHARMONIC-OSCILLATOR

For the motion in a one dimensional double well anharmonic potential w e derive upper bounds for the transition amplitudes induced by an exte rnal driving source when its frequency is in the domain where the mult isource transition becomes significant. The bounds found are less stri ngent compared to the existing bounds found in the literature regardin g the one source domination but in no case the amplitudes seem to beco me strong with increasing energy. The derivation and hence the validit y of similar bounds in realistic four dimensional field theory models remains to be seen.