Spectral distribution of nonlinear oscillators with nonlinear friction due to a medium

The analog of a quantum kinetic equation for the description of time correlation functions of singled out nonlinear oscillators interacting with a medium (e.g. local or quasi‐local vibrations in crystals) is obtained. Both the frictions, the linear and nonlinear one (the latter is due to decays with participation of two quanta of singled out oscillators), were taken into account. Spectral distributions of the correlation functions of the coordinates are found as well as those of occupation numbers. The essentially non‐Lorentzian shape of the spectral distribution and its dependence on interaction parameters and temperature are analysed.