The effect of an external perturbation on the energy spectrum of a mesoscopic quantum conductor can be described by a Brownian motion model developed by Dyson who wrote a Fokker-Planck equation for the evolution of the joint probability distribution of the energy levels. For weakly disordered conductors, which can be described by a Gaussian random matrix ensemble, the solution of the Fokker-Planck equation has recently been obtained to give the correlation of level densities at different

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... s and different parameter values. In this paper we generalize this calculation to the case of a q-random matrix ensemble which should be relevant for conductors at stronger disorder.