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Second wind of the Dulong-Petit Law at a quantum critical point

Renewed interest in 3He physics has been stimulated by experimental observation of non-Fermi-liquid behavior of dense 3He films at low temperatures. Abnormal behavior of the specific heat C(T) of two-dimensional liquid 3He is demonstrated in the occurrence of a T-independent term in C(T). To uncover the origin of this phenomenon, we have considered the group velocity of transverse zero sound propagating in a strongly correlated Fermi liquid. For the first time, it is shown that if two-dimensional liquid 3He is located in the vicinity of the quantum critical point associated with a divergent quasiparticle effective mass, the group velocity depends strongly on temperature and vanishes as T is lowered toward zero. The predicted vigorous dependence of the group velocity can be detected in experimental measurements on liquid 3He films. We have demonstrated that the contribution to the specific heat coming from the boson part of the free energy due to the transverse zero-sound mode follows the Dulong-Petit Law. In the case of two-dimensional liquid 3He, the specific heat becomes independent of temperature at some characteristic temperature of a few mK.