On the nature of the decay phonon spectrum in superfluid helium

Abstract

It is shown that the decay character of the phonon spectrum in superfluid helium is a consequence of the analyticity and parity of the boson self-energy as a function of energy and momentum. Previous self-consistent numerical calculations have shown that because of the strong interaction between the particles in Bose-Einstein condensate the normal and anomalous boson self-energies are analytical functions of the momentum and energy and on the mass shell, in the long-wavelength limit, they depend only on the squared momentum. It is shown on this basis that the phonon spectrum of a bose liquid is a decay spectrum in complete agreement with the experimental data on neutron scattering and the interaction of the high- and low-frequency phonons in superfluid helium.

Microscopic Theory of a System of Interacting Bosons-I : Basic Foundations and Superfluidity

“…The results of our theory can have meeting points with those of CMT [8,50] provided the energy corresponding to their concluded N(p) (Fig.4(B) is minimized. This point is concluded in our recent paper[79(c)] which not only reveals the absence of p=0 condensate but also demonstrates the possibility of N (=2, 3, ...) body correlations in superfluid state of a SIB; these correlations have been central to the recent developments in CMT [43][44][45][46]. The fact that our theory has been developed by solving its N-body Schrodinger equation in its standard differential form breaks the myth that such a solution is practically impossible to achieve.…”

“…Several research groups have been trying to revise our understanding of the superfluid state of a SIB, particularly, after the discovery of BEC in trapped dilute gases (TDG) and their detailed studies [40][41][42]. While some researchers [43][44][45][46] have been trying to establish the idea that the said state has a kind of generalized/composite condensate (p = 0 condensate + pair condensate + ..), others [47,48] have been making their efforts to underline the condensation of Cooper type pairs only. Developments in these directions are reviewed, recently, in several articles, viz., [49][50][51].…”