Modeling heat transfer at the nanoscale: A mixed quantum-classical approach

Abstract

Starting from the quantum-classical Liouville equation (QCLE), we derive a mixed quantum-classical expression for the heat current through a molecular junction that is coupled to two baths at different temperatures. In this approach, the molecular junction is treated quantum mechanically and the baths are treated classically. We apply this approach to study heat transfer in a nonequilibrium spin-boson model, which is composed of a two-level subsystem coupled to two independent bosonic heat baths. Specifically, we compute the time-dependent heat currents for a variety of subsystem-bath couplings and tunneling frequencies, using both the adiabatic and nonadiabatic solutions of the QCLE. Our results demonstrate that nonadiabatic effects are important over a wide parameter range and that this approach is capable of capturing the expected turnover behaviour in the steady-state heat current with increasing coupling strength. Owing to its rigorous foundation, this approach holds promise for simulations of nanoscale heat transfer in more realistic systems, for which fully quantum mechanical approaches are not computationally feasible.