Phonon Dispersion and Contribution to the Heat Capacity in Liquid He^4

概要

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The temperature dependent shift of the phonon excitation spectrum in liguid He^4, due to the phonon interactions in quantum hydrodynamics, is calculated over a wide range of momentum. It is found that in a limit of the small momentum the result is in agreement with previous papers, and in another limit of the large one the shift decreases logarithmical-ly with increasing momentum and turns into negative value beyond a critical momentum. Further a correction term to the specific heat, which is brought by this temperature dependent shift of the spectrum and gives a deviation from the T^3-law, is evaluated from the lowest order thermodynamical potential. The predicted contribution is proportional to T^7 and results in negligible magnitude at low-temperature and -pressure compared with the term γ-Tへえ(see Eq. (1・2) ) , which is dominant in the analysis of the experiments for the heat capacity by Phillips et al. As a result, the positive dispersion (γ<0) at zero temperature has not been altered by the evaluation obtained here.
理論物理学刊行会の論文
1972-05-25