Momentum of elementary excitations revisited: New variational approach to superfluid hydrodynamics of 4He

Abstract

The principal objectives of the paper are (i) to clarify the two-fluid picture of superfluid 4He by distinguishing and analysing the London-Tisza and Landau two-fluid models, (ii) to present a new derivation of the two-fluid equations within the framework of the Landau model by starting from Hamilton's variational principle in Lagrange form, and (iii) to critically discuss some generally accepted notions concerning momentum densities in the two-fluid models after characterizing the effective mass of the elementary excitations. It turns out that the effective mass density m ∗ of the elementary excitations is determined by m ∗ = ρρ n/ρ s . The superfluid velocity v s is shown to allow a dynamic, but not a kinematic interpretation in the Landau two-fluid model.