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Modeling of thermal transport in practical nanostructures requires makingtrade-offs between the size of the system and the completeness of the model. Westudy quantum heat transfer in a self-consistent thermal bath setup consistingof two lead regions connected by a center region. Atoms both in the leads andin the center region are coupled to quantum Langevin heat baths that mimic thedamping and dephasing of phonon waves by anharmonic scattering. This approachtreats the leads and the center region on same footing and thereby allows for asimple and physically transparent thermalization of the system, enabling alsoperfect acoustic matching between the leads and the center region. Increasingthe strength of the coupling reduces the mean free path of phonons andgradually shifts phonon transport from ballistic regime to diffusive regime. Inthe center region, the bath temperatures are determined self-consistently fromthe requirement of zero net energy exchange between the local heat bath andeach atom. By solving the stochastic equations of motion in frequency space andaveraging over noise using the general fluctuation-dissipation relation derivedby Dhar and Roy [J. Stat. Phys. 125, 801 (2006)], we derive the formula forthermal current, which contains the Caroli formula for phonon transmissionfunction and reduces to the Landauer-B\"uttiker formula in the limit ofvanishing coupling to local heat baths.

Thermal balance and quantum heat transport in nanostructures thermalized by local Langevin heat baths