Deformed damped harmonic oscillator

In the present paper we study the deformed harmonic oscillator in the presence of friction. We use the following time dependent Hamiltonian:H=e2γta2mp^1+λ2ℏq^22+e-2γtbmω22q^1-θ2ℏp^22,where λλ, θθ are real parameters. Hamiltonian of this type have been used to study dissipation in quantum mechanics.We find the exact propagator of the system. We find as well the time evolution of the coordinates and momenta operators. Finally, we investigate the thermodynamic properties of the system in Boltzmann statistics. We find the statistical density matrix and the specific heat.