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We study the energy dissipation rate in a mesoscopic system described by theparametrically-driven random-matrix Hamiltonian H[\phi(t)] for the case oflinear bias \phi=vt. Evolution of the field \phi(t) causes interleveltransitions leading to energy pumping, and also smears the discrete spectrum ofthe Hamiltonian. For sufficiently fast perturbation this smearing exceeds themean level spacing and the dissipation rate is given by the Kubo formula. Wecalculate the quantum correction to the Kubo result that reveals the originaldiscreteness of the energy spectrum. The first correction to the systemviscosity scales proportional to v^{-2/3} in the orthogonal case and vanishesin the unitary case.Comment: 4 pages, 3 eps figures, REVTeX

Quantum correction to the Kubo formula in closed mesoscopic systems