Spectrum of elementary excitations of the Bose system with account of pair correlations
National Science Center, Kharkov Institute of Physics and Technology 1 Akademicheskaya Str., Kharkiv 61108, Ukraine V.N. Karazin Kharkiv National University, 4 Svobody Sq., Kharkiv 61022, Ukraine
Received April 10, 2018, published online August 28, 2018
It is shown that for the quasiaverages of the products of field operators in the system of Bose particles the chain of equations can be obtained which is similar to the Bogolyubov chain in the theory of classical gases. In the case when it is sufficient to con-fine ourselves to taking into account the quasiaverages of one field operator and the products of two field operators, the closed system of dynamic equations at zero temperature is obtained which accounts for both the one-particle condensate and pair correlations. The spectrum of excitations in a spatially homogeneous state is explored and it is shown that the spectrum has two branches: the sound wave branch and the branch with an energy gap at zero momentum. The possibility is discussed of existence of the quasiparticle excitations with an energy gap in the super-fluid helium in connection with experiments on the absorption of microwave radiation.
Key words: Bose–Einstein condensate, anomalous and normal averages, pair correlations, sound branch of elementary excitations, elementary excitations with energy gap.