Crossover behavior of the thermal conductance and Kramers’ transition rate theory
Michael Zwolak1*, Kirill Velizhanin2, Subin Sahu3, Chih-Chun Chien4, Yonatan Dubi5
1Center for Nanoscale Science & Technology, National Institute of Standards & Technology, Gaithersburg, MD, United States of America
2Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, United States of America
3Department of Physics, Oregon State University, Corvallis, OR, United States of America
4School of Natural Sciences, University of California, Merced, Merced, CA, United States of America
5Department of Chemistry, Ben-Gurion University, Beer-Sheva, Israel
* presenting author:Michael Zwolak,
Heat transport plays opposing roles in nanotechnology, hindering the miniaturization of electronics on one hand and forming the core of novel heattronic devices on the other. Moreover, heat transport in one-dimensional nanostructures has become a central tool in studying the onset of Fourier’s law of heat conduction, a yet unresolved puzzle in theoretical physics. We study the paradigmatic setting of heat transport in one-dimensional systems, a lattice coupled to two heat baths held at different temperatures. Using both numerical and analytical tools, we demonstrate that the heat conductance displays a crossover behavior as the coupling to the thermal reservoirs is tuned. We provide evidence that this behavior is universal by examining harmonic, anharmonic, and disordered systems, and discuss the origin of this effect using an analogy with Kramers’ transition state theory for chemical reaction rates. This crossover behavior has important implications in the analysis of numerical results, and suggests a novel way to tune the conductance in nanoscale devices.

Keywords: Thermal transport, Kramers’ theory, Nanoscale science, Nonlinear systems, Extended reservoir method