Thermal rectification behaviour of some small quantum systems

Thermal rectification behaviors for some small quantum systems are studied by using the Lindblad master equation. From the underlying Hamiltonian dynamics of the composite quantum systems consisting of small quantum systems and reservoirs, Lindblad master equations are obtained by using certain approximations. Optimum operation parameters are determined for a single two-level and two two-level quantum systems. It is shown that there is no thermal rectification behavior when the contact between two reservoirs is a single harmonic oscillator or two harmonic oscillators Lindblad master equation and Hamiltonian dynamics is used separately to show that the zero rectification is due to the linearity of the dynamics of the oscillators and it is not the result of the approximations made when the Lindblad master equation is obtained.