Heat transport in low-dimensional systems
By A. Dhar. 2008
821 citations recorded by the source corpus.
Recent results on theoretical studies of heat conduction in low-dimensional systems are presented. These studies are on simple, yet non-trivial, models. Most of these are classical systems, but some quantum-mechanical work is also reported. Much of the work has been on lattice models corresponding to phononic systems, and some on hard-particle and hard-disc systems. A recently developed approach, using generalized Langevin equations and phonon Green's functions, is explained and several applications to harmonic systems are given. For interacting systems, various analytic approaches based on the Green–Kubo formula are described, and their predictions are compared with the latest results from simulation. These results indicate that for momentum-conserving systems, transport is anomalous in one and two dimensions, and the thermal conductivity κ diverges with system size L as κ ∼ L α. For one-dimensional interacting systems there is strong numerical evidence for a universal exponent α = 1/3, but there is no exact proof for this so far. A brief discussion of some of the experiments on heat conduction in nanowires and nanotubes is also given.
Subfields: Materials Chemistry, Mechanics of Materials
View Paper: https://www.semanticscholar.org/paper/1c95dbc373b7f64b5c185ff6b1769755a7ca1f15
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In Materials Chemistry
In Mechanics of Materials
Citations in the corpus
- Nonlinear Fluctuating Hydrodynamics for Anharmonic Chains (2013, background): “On this topic there is a huge literature, for which we have to refer to the reviews [4,5].”
- Stochastic thermodynamics, fluctuation theorems and molecular machines (2012, methodology): “Underdamped Langevin equations have been used to study heat transport through harmonic chains or lattices coupled at the end to heat reservoirs of different temperatures [65].”
- Colloquium: Phononic thermal properties of two-dimensional materials (2017, background): “Through many intensive numerical simulations (Lepri, Livi, and Politi, 2003, Dhar, 2008, Lepri, Livi, and Politi, 2016) and mathematical proofs (Prosen and Campbell, 2000),1 thermal conductivity is not found to be an intensive property.”
- Improvements on non-equilibrium and transport Green function techniques: The next-generation transiesta (2016, background): “with a large and growing community following the trend of electronic transport [89, 90].”
- Colloquium : Phononics: Manipulating heat flow with electronic analogs and beyond (2011, background): “Power spectra of FPU-β and FK lattices 21 References 21 I. INTRODUCTION When it comes to the task of transferring energy, nature has at its disposal tools such as electromagnetic radiation, conduction by electricity and also heat.”