Phonons in Nonlinear and Nonequilibrium Systems and Thermal Conductivity

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Abstract
Heat transport and dynamical properties of a one-dimensional monatomic lattice with large quartic potentials are investigated using the molecular dynamics method. Energy is transported not only through diffusive processes but also nondiffusive processes. The nondiffusive energy flow is assigned to modified KdV solitons, which decrease with propagation distance due to collisions with thermally excited phonons with very short wavelength. The behavior of energy spreading resembles anomalous diffusion due to the nondiffusive current within a critical region N cr or a critical time, τcr=N cr/\tv, where v denotes the velocity of the soliton. The diffusive behavior of energy spreading recovers beyond that region. Fourier's law is confirmed in the regime, and the thermal conductivity is found to be independent of local temperatures.