AN EXAMPLE OF THE DECOHERENCE APPROACH TO QUANTUM DISSIPATIVE CHAOS

Quantum chaos - the study of quantized nonintegrable Hamiltonian syste ms - is an extremely well-developed and sophisticated field. By contra st, very little work has been done in looking at quantum versions of s ystems which classically exhibit dissipative chaos. Using the decohere nce formalism of Gell-Mann and Hartle, I find a quantum mechanical ana log of one such system, the forced damped Duffing oscillator. I demons trate the classical limit of the system, and discuss its decoherent hi stories. I show that using decoherent histories, one can define not on ly the quantum map of an entire density operator, but can find an anal og to the Poincare map of the individual trajectory. Finally, I argue the usefulness of this model as an example of quantum dissipative chao s, as well as of a practical application of the decoherence formalism to an interesting problem.