TYPE-II QUANTUM CHAOS

A classification of quantum systems into three categories, type I, II and III, is proposed. The classification is based on the degree of sen sitivity upon initial conditions, and the appearance of chaos. The qua ntum dynamics of type I systems is quasi periodic displaying no expone ntial sensitivity. They arise, e.g., as the quantized versions of clas sical chaotic systems. Type II systems are obtained when classical and quantum degrees of freedom are coupled. Such systems arise naturally in a dynamic extension of the first step of the Born-Oppenheimer appro ximation, and;are of particular importance to molecular and solid stat e physics. Type II systems can show exponential sensitivity in the qua ntum subsystem. Type III systems are fully quantized systems which sho w exponential sensitivity in the quantum dynamics. No example of a typ e III system is currently established. This paper presents a,detailed discussion of a type II quantum chaotic system which models a coupled electronic-vibronic system. It is argued that type II systems are of i mportance for any field systems (not necessarily quantum) that couple to classical degrees of freedom.