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Crossover behavior of the thermal conductance and Kramers' transition rate theory

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Abstract
  • Kramers’ theory frames chemical reaction rates in solution as reactants overcoming a barrier in the presence of friction and noise. For weak coupling to the solution, the reaction rate is limited by the rate at which the solution can restore equilibrium after a subset of reactants have surmounted the barrier to become products. For strong coupling, there are always sufficiently energetic reactants. However, the solution returns many of the intermediate states back to the reactants before the product fully forms. Here, we demonstrate that the thermal conductance displays an analogous physical response to the friction and noise that drive the heat current through a material or structure. A crossover behavior emerges where the thermal reservoirs dominate the conductance at the extremes and only in the intermediate region are the intrinsic properties of the lattice manifest. Not only does this shed new light on Kramers’ classic turnover problem, this result is significant for the design of devices for thermal management and other applications, as well as the proper simulation of transport at the nanoscale.
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  • Velizhanin, K. A., Sahu, S., Chien, C. C., Dubi, Y., & Zwolak, M. (2015). Crossover behavior of the thermal conductance and Kramers’ transition rate theory. Scientific Reports, 5, 17506. doi:10.1038/srep17506
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  • 5
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  • K.A.V. was supported by the U.S. Department of Energy through the LANL/LDRD Program. Y.D. acknowledges support from the Israel Science Fund (grant No. 1256/14). S. Sahu acknowledges support under the Cooperative Research Agreement between the University of Maryland and the National Institute of Standards and Technology Center for Nanoscale Science and Technology, Award 70NANB10H193, through the University of Maryland.
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