Near-Field Heat Flow Between Two Quantum Oscillators

We calculate the exact steady-state heat flow between two Ohmically damped quantum oscillators 1 and 2, with natural frequency , interacting through their near-field dipole-dipole potential V. To keep them at nominally constant temperatures respectively, they have to be coupled to thermostats functioning in a way one must specify explicitly unless one assumes local thermal equilibrium, which would, inadequately as a rule, restrict the calculation to leading order in V. Here the thermostats are modelled as stretched strings, one end attached to the oscillator, and the other to an infinitely distant device ensuring that the string carries thermal noise appropriate to or in addition to whatever motion is enforced by the oscillator. Aiming at insight rather than numerics, we focus mainly on simple approximations by powers of and for weak damping in the essentially quantum low-temperature regime where . From it is easy to find the heat flux between two insulating Drude-modelled half-spaces.