SEMIQUANTUM CHAOS

We consider a system in which a classical oscillator is interacting wi th a purely quantum mechanical oscillator, described by the Lagrangian L = 1/2x2 + 1/2A2 - 1/2(m2 + e2A2)x2, where A is a classical variable and x is a quantum operator. With [x(t)] = 0, the relevant vaxiable f or the quantum oscillator is [x(t)x(t)] = G(t). The classical Hamilton ian dynamics governing the variables A(t), PI(A)(t), G(t), and PI(G)(t ) is chaotic so that the results of making measurements on the quantum system at later times are sensitive to initial conditions. This syste m arises as the zero momentum part of the problem of pair production o f charged scalar particles by a strong external electric field.