TABLE OF CONTENTS The single-mode relaxation time (SMRT) for a mode in a phonon system describes the temporal response of the system when that mode is excited and all other modes have their equilibrium populations. This is used in the BTE derivation of the phonon conductivity, as outlined in Figure 4.14. SMRT can be seen as being consistent with an exponential decay of the energy autocorrelations (Table 3.9) using the Green Kubo theory for thermal conductivity (Section 3.6 and will also be discussed in Sections 4.12-4.13). The limitation of this approach is that the underlying assumption (one mode activated and others at equilibrium) is never realized. This is because the natural decay of the energy in a mode occurs in the presence of other modes that are excited or diminished.
and temperature dependence 
.In SMRT approximation, each phonon mode ? has a single, effective phonon relaxation time ? p = ? p ( ? p , ?,T) representing the various scattering mechanisms.
The derivation presented in this section is based on that given by Callaway [53] and Holland [151]. The method presented can be applied to either a quantum or classical system.
The heat flux generated by a change in the...
