On the noise operator approach to quantized dissipative systems

Invoking complex classical coordinates and momenta a consistent Hamiltonian theory suitable for the quantization of dissipative systems has been developed previously. In another paper this formalism has been illustrated on the basis of a simple order parameter equation by means of density operator techniques. This quite naturally calls for a comparison with quantum noise operator techniques. The present paper is an attempt to satisfy these demands. Extensive use will be made of operator ordering techniques and quasi-classical Fokker-Planck equations. As before, a certain incompleteness in the extractable information is clearly exhibited. It will be observed that the two techniques do not produce similar results in a general dynamical state as a consequence of dissipation. However, in the stationary state and within certain approximations both methods do lead to identical conclusions for the order parameters statistics. It will be argued that within the present context in general noise operator techniques are to be favoured.