On the Relationships Between the Landau and London-Tisza Models of Liquid Helium II

The Landau (1941) picture of liquid helium II as a modified Debye model is critically compared with the London-Tisza picture of liquid helium II as a condensed Bose-Einstein assembly in an attempt to find some common features Two such common features are found, first that the criterion for Bose-Einstein condensation in a one-particle model is (partial differential S /partial differential N ) E,V less-than-or-eq, slant 0 or g =(partial differential F /partial differential N ) V,T gt-or-equal, slanted 0, a condition that can also be satisfied by the Debye model below a certain temperature Secondly, an assembly satisfying such a condition, is in principle, capable of being in thermodynamic equilibrium with a weakly adsorbed film or with free atoms of small energy It is also suggested that such atoms may make possible the observed phenomena of superfluid flow because their wave-functions are abnormally sensitive to small applied external fields of force, and some evidence in support of this is presented A numerical study of the Landau-Debye model shows that, in accordance with observed facts on helium II, its energy spectrum is probably modified considerably in channels of less than 10 -4 cm width It is also concluded that the Debye model is probably not a workable approximation near the λ-point, but that it is correct at sufficiently low temperatures