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Presented here is a nanowire model, consisting of coupled elastic membraneswith the purpose of investigating thermal transport in quasi-one-dimensionalquantum systems. The vibrations of each elastic membrane are quantized and theflow of the vibrational energy between adjacent membranes is allowed. The endsof the nanowire are attached to thermal baths held at different temperatures.We derived quantum master equation for energy flow across the nanowire andobtained thermal currents and other key observables. We study the effects of adisordered boundary on the thermal current by randomizing the membrane radii.We evaluate the model as a nanowire analogue as well as study the effects of adisordered boundary on thermal conductivity. The calculations show that themembrane lattice model demonstrates diameter phonon confinement and a severereduction in thermal conductivity due to surface roughness which ischaracteristic of semiconductor nanowires. The surface roughness also producesa length dependence of the thermal conductivity of the form $\kappa=\alphaL^{\beta}$, with $\beta$ dependent on disorder characteristics, in theotherwise ballistic regime. Finally, the parameters of the model are fitted toavailable experimental data for silicon nanowires and the results of thecalculations are assessed against the experimental data.

Coupled elastic membranes model for quantum heat transport in semiconductor nanowires