Criterion of superfluidity, elementary excitations, and heat capacity singularity in superfluid helium

Abstract

We proceed from the premise that the spectrum of elementary excitations in the normal component in Landau's theory of superfluidity should depend on the superfluid helium temperature. This leads to generalization of the Landau superfluidity criterion. On this basis, taking into account available experimental data on inelastic neutron scattering, it is shown that, in addition to phonon-roton excitations, there is one more type of elementary excitations in superfluid helium, which we called helons. The energy spectrum with such a momentum dependence was first proposed by Landau. The helon energy spectrum shape and its temperature dependence make it possible to explain the singular behavior of the heat capacity of superfluid helium near its phase transition to the normal state. PACS number(s): 67.25.de, 47.37.+q, 67.25.dj, 67.10.Fj According to the seminal phenomenological Landau theory [1,2], superfluid helium is a liquid consisting of superfluid and normal components. The superfluid component moves without friction and is not involved in the energy transport in the form of heat. The normal component moves with friction and is involved in heat transport. In this case, according to the Landau theory [1], the normal component is a gas of elementary excitations which are characterized by the dependence of the energy spectrum ε(p) on the momentum p. If the flow velocity V of the superfluid component reaches the critical velocity V cr , determined from the condition V cr = min (ε(p)/p) ,

Superfluids in Polymer Quantum Mechanics

“…the N-body system will be able to flow without any dissipation at all [64,65]. If the critical velocity is reached, then the superfluid phase will be broken, bringing into play the production and growth of excitations [66,67], as has been experimentally shown by studying either superfluid helium [68], ultracold bosons [64] or fermions [69].…”