Scaling of temperature-dependent thermal conductivities for one-dimensional nonlinear lattices

Abstract

In general nonlinear lattices, the existence of renormalized phonons due to the nonlinear interactions has been independently discovered by many research groups. Regarding these renormalized phonons as the energy carriers responsible for the heat transport, the scaling laws of temperature-dependent thermal conductivities of one-dimensional nonlinear lattices can be derived from the phenomenological effective phonon approach. For the paradigmatic nonlinear φ(4) lattice, κ(T)[proportionality]T(-1.35), which was numerically obtained more than a decade ago, can be well explained by the current approach. Most importantly, this approach is able to predict the scaling laws of temperature-dependent thermal conductivities of generalized nonlinear Klein-Gordon lattices. These theoretical predictions are compared by numerical simulations, and perfect agreements have been found.

Temperature dependence of thermal conductivities of coupled rotator lattice and the momentum diffusion in standard map

“…[62]. This power-law dependence of κ(T ) ∝ T −3.2 cannot be explained by the effective phonon theory which is able to predict the temperature dependent thermal conductivities for other typical 1D nonlinear lattices such as FPU-β lattice and generalized nonlinear Klein-Gordon lattices [68][69][70][71][72][73][74][75]. According to the effective phonon theory, the thermal conductivity for low temperature rotator lattice with Hamiltonian of Eq.…”

Triggering waves in nonlinear lattices: Quest for anharmonic phonons and corresponding mean-free paths

“…(Color online) (a) Phonon dispersion relation for a φ 4 nonlinear lattice at different temperatures. The dashed curves are obtained from renormalized phonon theory[48]. (b) Corresponding anharmonic phonon MFP behavior.…”

Temperature and frequency dependent mean free paths of renormalized phonons in nonlinear lattices

“…It also predicts the temperature dependence is k µ -( ) T T n 1 2 1 for H n lattices [16]. For lattices with on-site potentials, the effective phonon theory predicts for 1D f 4 lattice the temperature dependence is k µ -( ) T T 4 3 [11]. For general nonlinear Klein-Gordon lattices where f 4 lattice is a special example of n=4, this theory predicts the general temperature dependence as k µ -+ ( ) ( ) ( ) T T n n 4 2 2 [12].…”

“…In the regime of strong nonlinearity, the validity of conventional perturbative phonon transport theories is questionable. The phenomenological effective phonon theory [7,[11][12][13]16] is developed within the framework of renormalized phonons dedicated to the explanations of temperature dependence of thermal conductivities for nonlinear lattices. This theory can predict the actual exponents of the power-law dependence of thermal conductivities as the function of temperature for typical 1D nonlinear lattices.…”