Deformation of quantum oscillator and of its interaction with environment

A master equation for the deformed quantum harmonic oscillator interacting with a dissipative environment, in particular with a thermal bath, is derived in the microscopic model by using perturbation theory, for the case when the interaction is deformed. The coefficients of the master equation and of equations of motion for observables depend on the deformation function. The steady state solution of the equation for the density matrix in the number representation is obtained and shown that it satisfies the detailed balance condition. The equilibrium energy of the deformed harmonic oscillator, calculated in the approximation of small deformation, does not depend on the deformation of interaction operators