Thermal conductivity of nonlinear waves in disordered chains

Abstract

We present computational data on the thermal conductivity of nonlinear waves in disordered chains. Disorder induces Anderson localization for linear waves and results in a vanishing conductivity. Cubic nonlinearity restores normal conductivity, but with a strongly temperature-dependent conductivity $\kappa (T)$. We find indications for an asymptotic low-temperature $\kappa \sim T^4$ and intermediate temperature $\kappa \sim T^2$ laws. These findings are in accord with theoretical studies of wave packet spreading, where a regime of strong chaos is found to be intermediate, followed by an asymptotic regime of weak chaos (EPL 91 (2010) 30001).

8 pages, 3 figures

References in corpus (6)

• Direct observation of Anderson localization of matter-waves in a controlled disorder
• Heat Transport in low-dimensional systems
• Destruction of Anderson localization by a weak nonlinearity
• Absence of Wavepacket Diffusion in Disordered Nonlinear Systems
• The crossover from strong to weak chaos for nonlinear waves in disordered systems
• Effect of phonon-phonon interactions on localization

Cited by in corpus (8)

• Anderson localization or nonlinear waves? A matter of probability
• Nonlinear lattice waves in heterogeneous media
• Kinetic theory of nonlinear diffusion in a weakly disordered nonlinear Schrödinger chain in the regime of homogeneous chaos
• Thermal conductivities of one-dimensional anharmonic/nonlinear lattices: renormalized phonons and effective phonon theory
• Nonlinear Lattice Waves in Random Potentials
• Do nonlinear waves in random media follow nonlinear diffusion equations?
• Transport, correlations, and chaos in a classical disordered anharmonic chain
• Fragile Many Body Ergodicity