  A dissipative quantum system is treated here by coupling it with a heat bath
of harmonic oscillators. Through quantum Langevin equations and Ehrenfest's
theorem, we establish explicitly the quantum Duffing equations with a
double-well potential chosen. A quantum noise term appears the only driving
force in dynamics. Numerical studies show that the chaotic attractor exists in
this system while chaos is certainly forbidden in the classical counterpart.
