Crossover from Fermi-Pasta-Ulam to normal diffusive behaviour in heat conduction through open anharmonic lattices

Abstract

We study heat conduction in one, two and three dimensional anharmonic lattices connected to stochastic Langevin heat baths. The inter-atomic potential of the lattices is double-well type, i.e., $V_{\mathrm{DW}}(x)=k_2{x}^2/2+k_4{x}^4/4$ with $k_2<0$ and $k_4>0$. We observe two different temperature regimes of transport: a high-temperature regime where asymptotic length dependence of nonequilibrium steady state heat current is similar to the well-known Fermi-Pasta-Ulam lattices with an inter-atomic potential, $V_{\mathrm{FPU}}(x)=k_2{x}^2/2+k_4{x}^4/4$ with $k_2,k_4>0$. A low temperature regime where heat conduction is diffusive normal satisfying Fourier's law. We present our simulation results at different temperature regimes in all dimensions.

5 pages, 7 figures

References in corpus (14)

• Thermal conduction in classical low-dimensional lattices
• Dimensional crossover of thermal transport in few-layer graphene materials
• Heat Transport in low-dimensional systems
• Anomalous heat conduction in one dimensional momentum-conserving systems
• Finite thermal conductivity in 1d lattices
• On the anomalous thermal conductivity of one-dimensional lattices
• Exact results for anomalous transport in one dimensional Hamiltonian systems
• Heat transport in harmonic lattices
• Local Temperature and Universal Heat Conduction in FPU chains
• Heat transport and phonon localization in mass-disordered harmonic crystals
• Heat conduction in a three dimensional anharmonic crystal
• Heat conduction in 1D lattices with on-site potential
• Energy transport and correlation between two attractors connected by Fermi-Pasta-Ulam chain
• Crossover from ballistic to diffusive thermal transport in quantum Langevin dynamics study of a harmonic chain connected to self-consistent reservoirs

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