NONLINEAR RESONANCE AND CHAOS IN A DOUBLE SQUARE-WELL POTENTIAL - EFFECTS OF THE SYMMETRY OF THE POTENTIAL

We study the classical and the quantum dynamics of a particle in a dou ble square-well potential driven by a sinusoidal external force. Class ically, using both the renormalization technique and a computer simula tion, we compute the critical amplitude of the driving force at which the destruction of the KAM tori lying between two neighboring resonanc es occurs. The critical amplitude is seen to take on a higher value wh en the double well potential is symmetric with respect to its center t han when it is not. Similarly, our quantum calculations performed on t he same system indicate that the probability distribution tends to spr ead less and the entropy tends to be lower when the potential is symme tric. Investigation of the structure of the resonances in the classica l phase space and the corresponding quantum considerations yield a cle ar physical picture which establishes the relationship between the sym metry of the potential and the dynamics subjected to that potential.