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Concise Derivation of the Formulas for Lattice Thermal Conductivity
1.R. E. Peirels, Ann. Physik 3, 1055 (1929).
2.For an enumeration of these shortcomings, see R. J. Hardy, J. Math. Phys. 6, 1749 (1965).
3.R. J. Hardy, R. J. Swenson, and W. C. Schieve, J. Math. Phys. 6, 1741 (1965).
4.P. G. Klemens, in Solid State Physics, S. Seitz and D. Turnbull, Eds. (Academic Press, Inc., New York, 1958), Vol. 7, pp. 1–98, Eqs. (4.3) and (5.6);
4.and G. Leibfried, in Handbuch der Physik, S. Flügge, Ed. (Springer‐Verlag, Berlin, 1955), Vol. VII‐1, pp. 293–316, Eqs. (90.1), (90.5), and (93.6).
5.L. Van Hove, in La theorie des gas neutres et ionises (John Wiley & Sons, Inc., New York, 1960), pp. 151–183, Eq. (3.34).
6.R. J. Hardy and W. C. Schieve, J. Math. Phys. 7, 1439 (1966).
7.Equations (1)–(6) correspond to Eqs. (2.5), (2.8), (2.11), (2.17a), (4.1), and (4.2) in Ref. 3; see also footnote 21 in this reference.
8.Definition (6) of requires no restricting assumptions about the nature of since for one has for all X. However, for to be a useful quantity it must nowhere increase without bound as ε decreases and V increases. Although a proof of this is not given, the particular form of (5) suggests that it is probably true for a wide class of perturbations
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