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Exact reduced dynamics for a qubit in a precessing magnetic field and in the contact with a heat-bath

The two-level quantum system (qubit) in a precessing magnetic field and in contact with a heat bath is investigated. The exact reduced dynamics for the qubit in question is obtained. We apply the approach based on the block operator matrices theory, in contrast with the standard methods provided by the theory of the open quantum systems. We also present the solution of the Riccati operator equation associated with the Hamiltonian of the system. Next, we study the adiabatic approximation for the system under consideration using quantum fidelity as a way to measure validity of the adiabatic theory. We find that in the weak coupling domain the standard condition that ensures adiabatic behavior of the spin in the magnetic field also guarantees its adiabatic evolution in the open system variant of this model. Therefore, we provide the explicit example of the open quantum system that satisfies the adiabatic approximation firstly formulated for the closed quantum systems.