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Heat transport in overdamped quantum systems

We obtain an analytical expression for the heat current between two overdamped quantum oscillators interacting with local thermal baths at different temperatures. The total heat current is split into classical and quantum contributions. We show how to evaluate both contributions by taking advantage of the time scale separation associated with the overdamped regime, and without assuming the usual weak coupling and Markovian approximations. We find that non-trivial quantum corrections survive even when the temperatures are high compared to the frequency scale relevant for the overdamped dynamics of the system.