DYNAMICS OF BOSE-EINSTEIN CONDENSATE WITH ACCOUNT OF PAIR CORRELATIONS

It is shown that for the system of Bose particles it can be obtained the chain of equations for the quasiaverages of the products of field operators, being similar to the Bogolyubov-Born-Green-Kirkwood-Yvon chain in the theory of classical gases. For the case when it is sufficient to confine ourselves to taking account of the quasiaverages of only one field operator and the products of two field operators, the closed system of dynamic equations for Bose-Einstein condensate at zero temperature is obtained which accounts for the one-particle condensate and pair correlations. A spatially homogeneous state in the absence of the external field is considered and the spectrum of small oscillations of the condensate in this case with account of pair correlations is explored. It is shown that the spectrum of collective excitations has two branches: the sound wave branch and the branch with an energy gap at zero momentum. he first of the branches approaches the Bogolyubov spectrum at low momenta, and the second branch – at large momenta. It is discussed the possibility of existence of the quasiparticle excitations with an energy gap in the superfluid helium in connection with the experiment on the absorption of microwave radiation.