1) For a d-dimensional medium in which the lowest-lying vibrational modes of wavelength A have frequencies given by a dispersion relation of the form w ~ A-8, find expressions for the internal energy and the specific heat at constant volume using the Debye approximation. What is the behaviour of Cy (T) near absolute zero?

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1) For a d-dimensional medium in which the lowest-lying vibrational modes of wavelength ) have
frequencies given by a dispersion relation of the form w ~A-8, find expressions for the internal energy
and the specific heat at constant volume using the Debye approximation. What is the behaviour of
Cv (T) near absolute zero?
Transcribed Image Text:1) For a d-dimensional medium in which the lowest-lying vibrational modes of wavelength ) have frequencies given by a dispersion relation of the form w ~A-8, find expressions for the internal energy and the specific heat at constant volume using the Debye approximation. What is the behaviour of Cv (T) near absolute zero?
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