  On the basis of a coherent state representation of quantum noise operator and
an ensemble averaging procedure a scheme for quantum Brownian motion has been
proposed recently [Banerjee {\it et al}, Phys. Rev. E {\bf65}, 021109 (2002);
{\bf66}, 051105 (2002)]. We extend this approach to formulate reactive flux
theory in terms of quantum phase space distribution functions and to derive a
time dependent quantum transmission coefficient - a quantum analogue of
classical Kramers'-Grote-Hynes coefficient in the spirit of Kohen and Tannor's
classical formulation. The theory is valid for arbitrary noise correlation and
temperature. The specific forms of this coefficient in the Markovian as well as
in the non-Markovian limits have been worked out in detail for intermediate to
strong damping regime with an analysis of quantum effects. While the classical
transmission coefficient is independent of temperature, its quantum counterpart
has significant temperature dependence particularly in the low temperature
regime.
