Thermal Conductivity of an Anharmonic Crystal

An expression is obtained for the lattice thermal conductivity of an anharmonic crystal by the method of double-time Green's functions using the energy-flux operator propounded by Hardy. The study uses cubic and quartic anharmonic terms in the crystal Hamiltonian. It is found that the nondiagonal part of the energy-flux operator gives a finite contribution to the transport of energy, though its contribution is small compared to that from the diagonal part.