In the present work, we study heat transport through a one dimensional time-dependent nanomechanical system. The microscopic model consists of coupled chains of atoms, considering local and non-local interactions between particles. We show that the system presents different stationary transport regimes depending on the driving frequency, temperature gradients and the degree of locality of the interactions. In one of these regimes, the system operates as a phonon refrigerator, and its cooling performance is analyzed.
Based on a low frequency approach, we show that non-locality and its interplay with dissipation cause a decrease in cooling capacity. The results are obtained numerically by means of the Keldysh non-equilibrium Green’s function formalism.

Keywords: Transport processes, Non-local interaction, Heat conduction, Quantum refrigeration.