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I am reading about Boltzmann equation and I am having a hard time making a link between elastodynamics and phonon equations. Clearly there should be a limit where both are one and the same, isn't it? How is the thermal conductivity or the time-relaxation rate related to the elastic coefficients of wave propagation in linear elasticity?

Or are both theories completely unrelated? Any hints on the limit in which microscopic theories link to acoustics would be great.

I am reading about Boltzmann equation and I am having a hard time making a link between elastodynamics and phonon equations. Clearly there should be a limit where both are one and the same, isn't it? How is the thermal conductivity or the time-relaxation rate related to the elastic coefficients of wave propagation in linear elasticity?

Or are both theories completely unrelated? Any hints on the limit in which microscopic theories link to acoustics would be great.

I am not looking on why the macroscopic model is wrong but under what limit one recovers this model from the microscopic model and how are the microscopic coefficients tied to the macroscopic ones.

I am reading about Boltzmann equation and I am having a hard time making a link between elastodynamics and phonon equations. Clearly there should be a limit where both are one and the same or not? How is the thermal conductivity or the time-relaxation rate related to the elastic coefficients of wave propagation in linear elasticity?

Or are both theories completely unrelated? Any hints on the limit in which microscopic theories link to acoustics would be great.

I am reading about Boltzmann equation and I am having a hard time making a link between elastodynamics and phonon equations. Clearly there should be a limit where both are one and the same, isn't it? How is the thermal conductivity or the time-relaxation rate related to the elastic coefficients of wave propagation in linear elasticity?

Or are both theories completely unrelated? Any hints on the limit in which microscopic theories link to acoustics would be great.

I am reading about Boltzmann equation and I am having a hard time making a link between elastodynamics and phonon equations. Clearly there should be a limit where both are one and the same or not? How is the thermal conductivity or the time-relaxation rate related to the elastic coefficients of wave propagation in linear elasticity?

Or are both theories completely unrelated?

I am reading about Boltzmann equation and I am having a hard time making a link between elastodynamics and phonon equations. Clearly there should be a limit where both are one and the same or not? How is the thermal conductivity or the time-relaxation rate related to the elastic coefficients of wave propagation in linear elasticity?

Or are both theories completely unrelated? Any hints on the limit in which microscopic theories link to acoustics would be great.