Numerical analysis of thermal conduction in a nonlinear lattice with nonlocality

We propose a unique one-dimensional (1D) nonlinear lattice with nonlocality. This lattice is referred to as the umklapp-free lattice (UFL), in which no umklapp processes occur. The absence of umklapp processes is mathematically guaranteed from the viewpoint of crystal momentum. In previous works, a methodology for constructing the UFL was presented, and a UFL with quartic nonlocal nonlinearity was proposed. We newly apply a cubic nonlocal nonlinearity to the UFL, rigorously determined to eliminate umklapp processes. A nonequilibrium steady-state simulation is also performed to evaluate the thermal transport properties of the UFL. It is revealed that thermal resistance, which corresponds to umklapp processes, is suppressed as the range of nonlocality increases.