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Updated: Apr 12, 2026

Characterization of Thermal Transport in One-dimensional Solid Materials
Published on: January 26, 2014
Thermal transport in phononic Cayley-tree networks
Huanan Li1, Tsampikos Kottos1, Boris Shapiro2
1Department of Physics, Wesleyan University, Middletown, Connecticut 06459, USA.
Abstract:
We analytically investigate the heat current I and its thermal fluctuations Δ in a branching network without loops (Cayley tree). The network consists of two types of harmonic masses: vertex masses M placed at the branching points where phononic scattering occurs and masses m at the bonds between branching points where phonon propagation takes place. The network is coupled to thermal reservoirs consisting of one-dimensional harmonic chains of coupled masses m. Due to impedance mismatch phenomena, both I and Δ are non-monotonic functions of the mass ratio μ=M/m. Furthermore, we find that in the low-temperature limit the thermal conductance approaches zero faster than linearly due to the small transmittance of the long-wavelength modes.
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