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

TL;DR

This study measures the dispersion relation of superfluid helium-4's elementary excitations across a wide range of conditions, compares it with theoretical predictions, and uses it to accurately calculate thermodynamic properties up to 1.3 K.

Contribution

It provides a comprehensive experimental determination of the dispersion relation and develops an analytical and numerical approach to calculate thermodynamic properties from it.

Findings

Dispersion relation matches dynamic many-body theory predictions.

Transition from anomalous to normal dispersion with pressure is characterized.

Calculated specific heat agrees with measurements below 0.85 K.

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.