Effective phonon theory of heat conduction in 1D nonlinear lattice chains

Abstract

This thesis deals with the classical heat conduction of 1D nonlinear lattice. A new theory of heat conduction, Effective Phonon Theory, has been developed based on effective phonons. The effective phonons are renormalized phonons due to the nonlinear interactions. For lattices without on-site potential, the resulted effective phonons are acoustic-like. For lattices with on-site potential, the effective phonons are optical-like. The normal/anomalous heat conduction of lattices with/without on-site potential is well explained by this theory.A correlation between nonlinearity strength and heat conductivity has been found through numerical simulations. By incarnating this nonlinearity strength into the expression of the mean-free-path of effective phonons, the temperature dependence of heat conductivity is explained consistently for general 1D lattices with and without on-site potential.The effective phonon theory is applied to the 1D $\phi^4$ lattice. The parameter-dependent heat conductivities beyond the size and temperature have been derived and compared with numerical simulations.