Heat-current correlation loss induced by finite-size effects in a one-dimensional nonlinear lattice

The Green-Kubo formula provides a mathematical expression for heat conductivity in terms of integrals of the heat-current correlation function, which should be calculated in the thermodynamic limit. In finite systems this function generally decreases, i.e., it decays faster than it does in infinite systems. We compared the values of the correlation function in a one-dimensional purely quartic lattice with various lengths, and found that this loss is much smaller than is conventionally estimated. By studying the heat diffusion process in this lattice, we found that, in contrast to the conventional belief, the collisions between sound modes do not noticeably affect the current correlation function. Therefore, its loss being surprisingly small can be well understood. This finding allows one to calculate the heat conductivity in a very large system with desirable accuracy by performing simulations in a system with much smaller size, and thus greatly broadens the application of the Green-Kubo method.