Improvement of variational bounds on lattice thermal conductivity by scaling and Ritz procedures

The systematic improvement of complementary variational bounds on lattice thermal conductivity by scaling and Ritz procedures are discussed. A calculation is performed to show that a Ritz procedure gives a well converged limit of the improvement of a lower bound on the conductivity. This limit is found to be a far better result than a single scale factor yields. It is suggested that only a very small number of terms in the Ritz procedure are needed to reach the above limit when a much better lower bound is improved. The well converged limit is compared with results of various methods of calculating thermal conductivity using the same physical model.