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Introduction to Phonon Hydrodynamics

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Part of the NATO ASI Series book series (ASIB,volume 124)


The subject of phonon hydrodynamics is the study of the collective behavior of the interacting phonon system at low frequencies and long wavelengths. For most problems in lattice dynamics the enharmonic interactions among the phonons of a pure dielectric are weak perturbations, which have the effect of a slight temperature dependent frequency shift of the phonons in the harmonic approximation and of introducing a finite lifetime. These quantities were calculated by Maradudin and Fein (1962) by applying many-body techniques to the phonon system. Lorentzian line shapes f or the response functions, which are measured in various scattering experiments, are very often satisfactory descriptions of the result of these measurements. At low frequencies, however, in the first sound region (Cowley 1967), the frequency Ω is much less than the inverse lifetime Γ of mostof the phonons in the crystal. Therefore, the latter are able to follow the low-frequency excitation to a certain extent. If the low-frequency excitation is connected with a slowly varying temperature or density, the distribution of thermal phonons will adjust to the local values of these thermodynamic variables, since many enharmonic processes among the thermal phonons take place during one period of the excitation. Such phenomena, which are connected to space and time dependent phonon density fluctuations and are therefore similar to the situation in gases or liquids, are the subject of interest in phonon hydrodynamics.


  • Green Function
  • Phonon Density
  • Phonon Transport
  • Thermal Phonon
  • Retarded Green Function

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© 1985 Plenum Press, New York

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Klein, R. (1985). Introduction to Phonon Hydrodynamics. In: Bron, W.E. (eds) Nonequilibrium Phonon Dynamics. NATO ASI Series, vol 124. Springer, Boston, MA.

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  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4612-9513-6

  • Online ISBN: 978-1-4613-2501-7

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