Vibrational relaxation in the Kubo oscillator: stochastic pumping of heat

We present a model for a molecular level heat pump that operates when a stochastic time dependent force modulates the molecular vibrational energies. The model consists a molecular unit, represented by a Kubo oscillator, coupled to two solids characterized by distinct spectral properties and kept at unequal temperatures. In the fast modulation limit we derive expressions for the vibrational energy transition rates in the Kubo oscillator, and show that they do not trivially correspond to the population transition rates, unlike the field-free (or adiabatic) limit. We discuss the operation principle of the pump and manifest, analytically and numerically, directing of heat against a temperature gradient for a broad range of system and bath parameters. The present formalism could also describe a unidirectional exciton energy flow in a metal-molecule-metal junction under random noise.