Theory of a many-boson system with deformed Heisenberg algebra

TL;DR

This paper develops a theoretical framework for liquid helium-4 using deformed Heisenberg algebra to incorporate many-body correlations, leading to improved estimates of ground state properties and excitation spectra.

Contribution

It introduces a deformation of the Heisenberg algebra to account for three- and four-particle correlations in liquid helium-4, connecting theoretical parameters with experimental data.

Findings

Estimated ground state energy aligns with experimental data.

Reconstructed excitation spectrum matches observed behavior.

Derived interaction potential consistent with helium atom interactions.

Abstract

We propose to consider nonlinear fluctuations in the theory of liquid $^{4}$He deforming the commutation relations between the generalized coordinates and momenta. Generalized coordinates are coefficients of density fluctuations of Bose particles. The deformation parameter takes into account the effects of three- and four-particle correlations in the behavior of a 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 excitation spectrum and the potential of interaction between the helium atoms are recovered.