8,198 research outputs found
Thermal Transport at the Nanoscale: A Fourier\u27s Law vs. Phonon Boltzmann Equation Study
Steady-state thermal transport in nanostructures with dimensions comparable to the phonon mean-free-path is examined. Both the case of contacts at different temperatures with no internal heat generation and contacts at the same temperature with internal heat generation are considered. Fourier’s Law results are compared to finite volume method solutions of the phonon Boltzmann equation in the gray approximation. When the boundary conditions are properly specified, results obtained using Fourier’s Law without modifying the bulk thermal conductivity are in essentially exact quantitative agreement with the phonon Boltzmann equation in the ballistic and diffusive limits. The errors between these two limits are examined in this paper. For the four cases examined, the error in the apparent thermal conductivity as deduced from a correct application of Fourier’s Law is less than 6%. We also find that the Fourier’s Law results presented here are nearly identical to those obtained from a widely used ballistic-diffusive approach, but analytically much simpler. Although limited to steady-state conditions with spatial variations in one dimension and to a gray model of phonon transport, the results show that Fourier’s Law can be used for linear transport from the diffusive to the ballistic limit. The results also contribute to an understanding of how heat transport at the nanoscale can be understood in terms of the conceptual framework that has been established for electron transport at the nanoscale
Fourier's Law: insight from a simple derivation
The onset of Fourier's law in a one-dimensional quantum system is addressed
via a simple model of weakly coupled quantum systems in contact with thermal
baths at their edges. Using analytical arguments we show that the crossover
from the ballistic (invalid Fourier's law) to diffusive (valid Fourier's law)
regimes is characterized by a thermal length-scale, which is directly related
to the profile of the local temperature. In the same vein, dephasing is shown
to give rise to a classical Fourier's law, similarly to the onset of Ohm's law
in mesoscopic conductors.Comment: 4+ pages, references and discussions adde
Quantum transport efficiency and Fourier's law
We analyze the steady-state energy transfer in a chain of coupled two-level
systems connecting two thermal reservoirs. Through an analytic treatment we
find that the energy current is independent of the system size, hence violating
Fourier's law of heat conduction. The classical diffusive behavior in Fourier's
law of heat conduction can be recovered by introducing decoherence to the
quantum systems constituting the chain. Implications of these results on energy
transfer in biological light harvesting systems, and the role of quantum
coherences and entanglement are discussed.Comment: 6 pages, 4 figure
Reconstructing Fourier's law from disorder in quantum wires
The theory of open quantum systems is used to study the local temperature and
heat currents in metallic nanowires connected to leads at different
temperatures. We show that for ballistic wires the local temperature is almost
uniform along the wire and Fourier's law is invalid. By gradually increasing
disorder, a uniform temperature gradient ensues inside the wire and the thermal
current linearly relates to this local temperature gradient, in agreement with
Fourier's law. Finally, we demonstrate that while disorder is responsible for
the onset of Fourier's law, the non-equilibrium energy distribution function is
determined solely by the heat baths
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