On the Structure of the Superfluid State and Quasiparticle Spectrum in a Bose Liquid with a Suppressed Bose–Einstein Condensate

Calculation of the one-particle and two-particle condensates in He-II at T=0

“…As far as we know, the higher s-particle condensates (s ≥ 3) were not calculated previously. The amount of 1PC in He-II at T = 0 was found in many works [2,14,18,20]- [24,11] (though only in [14,18,23,24] it was done without free parameters), and the theory agrees with the experiment on the whole. The amount of 2PC in He-II is still unknown.…”

“…In the 1S-approximation, the amount of 1PC can be simply found from (10), (11), and (19). For the structure factor S(k), we use the smoothed experimental data from [36], which is, perhaps, the most exact.…”

“…The sum of one-particle condensate (1PC), two-particle condensate (2PC) and higher s-particle condensates is usually referred to as the composite condensate. Knowing the structure of the composite condensate in He-II is, without doubt, of great importance [1]- [11]. Except for a purely cognitive interest, it also has a "practical" side, namely, in the field-theoretic approaches to the modelling of He-II microstructure [1,4,5,11], the quasiparticle spectrum of He-II is explicitly expressed through the amount of the 1PC and 2PC, and the dependence on higher condensates is also not excluded.…”

“…Except for a purely cognitive interest, it also has a "practical" side, namely, in the field-theoretic approaches to the modelling of He-II microstructure [1,4,5,11], the quasiparticle spectrum of He-II is explicitly expressed through the amount of the 1PC and 2PC, and the dependence on higher condensates is also not excluded. Of interest is the question whether all of He-II atoms belong to the composite condensate at T = 0, as was suggested in [7,8,11]. The superfluidity of He-II by itself is probably [3,12] caused by an off-diagonal long-range order (ODLRO).…”

Calculation of the He-II quasiparticle spectrum by the method of collective variables

“…The potential U (r) in a zeroth-order approximation was obtained in work 25 earlier. The potential calculated by us approximately agrees with those obtained in works 5,11,33,34 , but not with Aziz's potential 35 , which possesses a very high barrier of repulsion U (r = 0) ∼ 10 6 K. This discrepancy might be caused by the efficiency of the potential that describes the interaction between He 4 atoms at small distances, as well as by different modeling of such interaction. It is not improbable that some processes (e.g., the scattering of He 4 atoms) are better described by Aziz's potential, while others (in particular, the calculation of Ψ 0 , ψ k , and the E(k) spectrum) by a potential with a much smaller effective barrier U (0) ∼ 100 K. One can see from Fig.…”