Riccati equation and the problem of decoherence

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The block operator matrix theory is used to investigate the problem of a single qubit. We will establish a connection between the Riccati operator equation and the possibility of obtaining an exact reduced dynamics for the qubit in question. The model of the half spin particle in the rotating magnetic field coupling with the external environment is discussed. We show that the model defined in such a way can be reduced to a time independent problem.