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The paper deals with the problem of dynamics of externally driven openquantum systems. Using the path integral methods we found an analyticalexpression for time-dependent density matrix of two externally driven coupledquantum oscillators interacting with different baths of oscillators. It isshown that at the zeroing of external forces the density matrix becomesidentical to the previously obtained one for freely developing coupledoscillators. Mean values of observables are computed by using the Hermitianpart of the matrix. All elements of the covariance matrix composed bycoordinates and momenta of two driven coupled oscillators are calculated. Thetime-dependent mean values, dispersions and covariances of coordinates ofcoupled oscillators at given external forces are numerically studied. It isshown that the larger the coupling constant the larger is the disturbances ofthe second oscillator due to external action on the first oscillator. Coupleddynamics of forced oscillators at relatively large coupling constant isdemonstrated at different thermodynamic conditions.

Dynamics of two externally driven coupled quantum oscillators interacting with separate baths based on path integrals