9780030839931, Chapter 23, Problem 2P

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Chapter 23, Problem 2P Problem Low Temperature Specific Heat in d-Dimensions, and for Nonlinear Dispersion Laws (a) Show that Eq. (23.36), for the density of normal modes in the Debye approximation, gives the exact (within the harmonic approximation) leading low-frequency behavior of g(w), provided that the velocity C is taken to be that given in Eq. (23.18). (b) Show that in a d-dimensional harmonic crystal, the low-frequency density of normal modes varies as wd- 1. (c) Deduce from this that the low-temperature specific heat of a harmonic crystal vanishes as Td in d dimensions. (d) Show that if it should happen that the normal mode frequencies did not vanish linearly with but as kv then the low-temperature specific heat would vanish as Td/v, in d dimensions. Step-by-step solution There is no solution to this problem yet. Get help from a Chegg subject expert. Ask an expert