Phenomenological approach to classical and quantum relaxation of the harmonic oscillator

A phenomenological approach for construction of the Markovian master equation describing the relaxation of the harmonic oscillator to the equilibrium at temperatureT is presented. A superoperator formalism built up by analogy with the second quantization method of quantum mechanics is proposed for the formulation of both the classical and quantum master equations. The quantum-field-theoretical methods are used for the calculation of the mean values of the physical quantities and for the solution of the master equations.