Optical Lindblad operator in non-equilibrium thermo field dynamics

The Lindblad operator of the Markovian quantum master equation for an oscillator system is diagonalized by means of linear transformations of annihilation and creation operators in non-equilibrium thermo field dynamics. When the linear attenuation and amplification processes are considered, the left and right eigenstates of the Lindblad operator are constructed in terms of the transformed operators. In the linear attenuation process, the results are compared with those obtained by the damping base of the Lindblad superoperator. The base describing the time-evolution of the linear amplification process is derived and compared with the damping base. The method for diagonalizing the Lindblad operator is useful for calculating average values of physical quantities in the quantum Markovian process.