Condensed Matter Physics, 2015, vol. 18, No. 3, p. 33002
DOI:10.5488/CMP.18.33002           arXiv:1503.04746

Title: The theory of a many boson system with the deformed Heisenberg algebra
  I.O. Vakarchuk (Department for Theoretical Physics, Ivan Franko National University of Lviv, 12 Dragomanov St., 79005 Lviv, Ukraine) ,
  G.I. Panochko (College of Natural Sciences, Ivan Franko National University of Lviv, 107 Tarnavsky St., 79010 Lviv, Ukraine) ,

We propose to consider nonlinear fluctuations in the theory of liquid 4He deforming the commutation relations between the generalized coordinates and momenta. The generalized coordinates are the coefficients of the density fluctuations of the Bose particles. The deformation parameter takes into account effects of three- and four-particle correlations in the behavior of the system. This parameter is defined from the experimental values of the elementary excitation spectrum and the structure factor extrapolated to T=0 K. The numerical estimation of the ground state energy and the Bose condensate fraction is made. The elementary exitation spectrum and the potential of interaction between the helium atoms are recovered.

Key words: deformed Heisenberg algebra, collective variables, elementary exitation spectrum of liquid 4He, Bose-condensate
PACS: 05.30.Jp, 02.40.Gh, 67.25.-k, 67.25.dt, 03.65.-w

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