Heat conduction in chains of non-locally coupled harmonic oscillators: mean-field limit
arXiv:2111.01332 · doi:10.1103/PhysRevE.105.054149
Abstract
We consider one-dimensional systems of all-to-all harmonically coupled particles with arbitrary masses, subject to two Langevin thermal baths. The couplings correspond to the mean-field limit of long-range interactions. Additionally, the particles can be subject to a harmonic on-site potential to break momentum conservation. Using the non-equilibrium Green operator formalism, we calculate the transmittance, the heat flow and local temperatures, for arbitrary configurations of masses. For identical masses, we show analytically that, the heat flux decays with the system size , as , regardless of the conservation or not of the momentum, and of the introduction or not of a Kac factor. These results describe in good agreement the thermal behavior of systems with small heterogeneity in the masses.
arXiv comment6 pages, 5 figures
References in corpus (40)
- Thermal conduction in classical low-dimensional lattices
- Phononics: Manipulating heat flow with electronic analogs and beyond
- Thermal diode: Rectification of heat flux
- Statistical mechanics and dynamics of solvable models with long-range interactions
- Heat Transport in low-dimensional systems
- Anomalous heat conduction in one dimensional momentum-conserving systems
- Non-Gaussian equilibrium in a long-range Hamiltonian system
- Inequivalence of ensembles in a system with long range interactions
- Thermal rectification and negative differential thermal resistance in lattices with mass gradient
- Finite thermal conductivity in 1d lattices
- Nonequilibrium Statistical Mechanics of Systems with Long-Range Interactions: Ubiquity of Core-Halo Distributions
- Breaking of ergodicity and long relaxation times in systems with long-range interactions
- Heat conduction in the disordered harmonic chain revisited
- Heat transport in low dimensions: introduction and phenomenology
- Long-range interacting rotators: connection with the mean--field approximation
- Anomalous Heat Diffusion
- Anomalous Heat Diffusion
- Canonical solution of a system of long-range interacting rotators on a lattice
- On the diffusive anomalies in a long-range Hamiltonian system
- Anomalous heat transport in classical many-body systems: overview and perspectives
- The world of long-range interactions: A bird's eye view
- Increasing thermal rectification: Effects of long range interactions
- Heat transport in oscillator chains with long-range interactions coupled to thermal reservoirs
- Thermal transport in the Fermi-Pasta-Ulam model with long-range interactions
- 1D momentum-conserving systems: the conundrum of anomalous versus normal heat transport
- Role of the range of the interactions in thermal conduction
- Thermal transport in long-range interacting Fermi-Pasta-Ulam chains
- Ingredients for an efficient thermal diode
- Energy current correlation in solvable long-range interacting systems
- Fourier's law from a chain of coupled planar harmonic oscillators under energy conserving noise
- Energy transport in the presence of long-range interactions
- Equilibrium time-correlation functions of the long-range interacting Fermi-Pasta-Ulam model
- Dynamics and physical interpretation of quasi-stationary states in systems with long-range interactions
- Heat transport in long-ranged anharmonic oscillator models
- Nonextensive scaling in a long-range Hamiltonian system
- Phase transitions in simplified models with long-range interactions
- Thermal conductance of one dimensional disordered harmonic chains
- Random Matrix Theory approach to Mesoscopic Fluctuations of Heat Current
- Localization effects due to a random magnetic field on heat transport in a harmonic chain
- Temperature gradient and Fourier's law in gradient-mass harmonic systems
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