Heat transport in nonlinear lattices free from the Umklapp process

Abstract

We construct one-dimensional nonlinear lattices having the special property such that the Umklapp process vanishes and only the normal processes are included in the potential functions. These lattices have long-range quartic nonlinear and nearest neighbor harmonic interactions with/without harmonic on-site potential. We study heat transport in two cases of the lattices with and without harmonic on-site potential by non-equilibrium molecular dynamics simulation. It is shown that the ballistic heat transport occurs in both cases, i.e., the scaling law $\kappa \propto N$ holds between the thermal conductivity $\kappa$ and the lattice size $N$. This result directly validates Peierls's hypothesis that only the Umklapp processes can cause the thermal resistance while the normal one do not.

arXiv comment11 pages, 6 figures, 1 table

References in corpus (16)

• Thermal conduction in classical low-dimensional lattices
• Heat conduction in one dimensional chains
• Finite thermal conductivity in 1d lattices
• Heat conduction in one dimensional nonintegrable systems
• Heat conduction in the diatomic Toda lattice revisited
• Bulk Properties of Anharmonic Chains in Strong Thermal Gradients: Non-Equilibrium ${\varphi }^4$ Theory
• Energy transport in anharmonic lattices close and far from equilibrium
• 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
• Thermal transport in long-range interacting Fermi-Pasta-Ulam chains
• Fourier law in a momentum-conserving chain
• Memory Effects and Heat Transport in One-dimensional Insulators
• Coexistence of ballistic and Fourier regimes in the $\beta$-FPUT lattice
• Transport in perturbed classical integrable systems: the pinned Toda chain
• Construction of nonlinear lattice with potential symmetry for smooth propagation of discrete breather
• Heat transport in long-ranged anharmonic oscillator models

Cited by in corpus (3)

• Heat transport and rectification via quantum statistical and coherence asymmetries
• Construction of cubic nonlinear lattice free from umklapp processes
• Recent progress on thermal transport in one-dimensional long-range interacting Fermi-Pasta-Ulam-Tsingou lattice systems