An application of non-communicative complementary variational principles to the calculation of phonon thermal conductivity

The complementary variation principle is used to obtain sequences of lower and upper bounds on the phonon thermal conductivity. In comparison with previous work the present analysis has the advantage that the two parts of the collision operator are taken to be non-commutative. The convergence of the sequences of lower and upper bounds as well as the best way of decomposing the collision operator in each case are explored in a more rigorous and general manner than has been done hitherto.