The narrow peak on the frequency dependance of the susceptibility of the harmonical oscillator in contact with thermostat with bosonic excitations. Exactly-solvable model

The relaxation of the harmonical oscillator, being in contact with the thermostat whose excitations can be treated as bosons is studied. An exact temporary behavior of the inverse oscillator’s temperature is obtained. In low interaction limit the temperature behavior is exponential. When the interaction is increasing the temporary behavior display oscillations. Narrow peak of the oscillator susceptibility is discovered. The exact solution obtained is compared with Bloch-Redfild approximation.