The dispersion relation of Landau elementary excitations and the thermodynamic properties of superfluid ${}^4$He

Abstract

The dispersion relation $\epsilon (k)$ of the elementary excitations of superfluid ${}^4$He has been measured at very low temperatures, from saturated vapor pressure up to solidification, using a high flux time-of-flight neutron scattering spectrometer equipped with a high spatial resolution detector (10${}^5$ 'pixels'). A complete determination of $\epsilon (k)$ is achieved, from very low wave-vectors up to the end of Pitaeskii's plateau. The results compare favorably in the whole the wave-vector range with the predictions of the dynamic many-body theory (DMBT). At low wave-vectors, bridging the gap between ultrasonic data and former neutron measurements, the evolution with the pressure from anomalous to normal dispersion, as well as the peculiar wave-vector dependence of the phase and group velocities, are accurately characterized. The thermodynamic properties have been calculated analytically, developing Landau's model, using the measured dispersion curve. A good agreement is found below 0.85 K between direct heat capacity measurements and the calculated specific heat, if thermodynamically consistent power series expansions are used. The thermodynamic properties have also been calculated numerically; in this case, the results are applicable with excellent accuracy up to 1.3 K, a temperature above which the dispersion relation itself becomes temperature dependent.

35 pages, 59 figures; Supplemental Material: Text, Tables, data files

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