Finite Heat conduction in 2D Lattices

This paper gives a 2D hamonic lattices model with missing bond defects, when the capacity ratio of defects is enough large, the temperature gradient can be formed and the finite heat conduction is found in the model. The defects in the 2D harmonic lattices impede the energy carriers free propagation, by another words, the mean free paths of the energy carrier are relatively short. The microscopic dynamics leads to the finite conduction in the model. PACS numbers: 44.10. +I, 05.45.Jn, 05.60.-k, 05.70.Ln The study of heat conduction in models of insulating solids is a rather old and debated problem, and the more general problem is one of understanding the nonequilibrium energy current carrying state of a many body system. The most of the work on heat conduction investigated the process of heat transport in 1D lattices. The different models have been studied for obtaining Fourier’s law, several kinds of factors have been taken into account in the models, such as the nonlinearity, on-site potentials, mass disorder and etc. Then the typical 1D lattices Hamiltonian is