Quantum Smoluchowski equation

The strong friction limit of the Caldeira-Leggett model for quantum-Brownia n motion is analyzed. Jh this Smoluchowski limit the density operator of th e Brownian particle is essentially diagonal in coordinate, and the diagonal element satisfies the classical Smoluchowski equation. This result cannot be obtained from the master equations that have been proposed for quantum B rownian motion, whether or not these equations are of Lindblad form.