Internal energy of many-boson system with three- and four-particle direct correlations taken into account

TL;DR

This paper calculates the internal energy of an interacting Bose system considering three- and four-particle correlations across a wide temperature range, aiding in understanding liquid helium-4's thermodynamics.

Contribution

It introduces a method to compute the energy of many-boson systems including higher-order correlations, extending previous models to better match experimental data.

Findings

Energy expressions match known ground state results at low temperatures.

Results can be used to numerically analyze heat capacity of liquid helium-4.

Method accounts for three- and four-particle correlations in energy calculations.

Abstract

In this paper we calculate kinetic, potential and full energy with three- and four-particle direct correlations taken into account at wide temperature region on the base of the density matrix of the interacting Bose-particles [I. O. Vakarchuk, O. I. Hryhorchak, Journ. Phys. Stud. {\bf 3}, 3005 (2009)]. In the low temperature limit the obtained expression for the full energy is equal to the wellknown expression for ground state energy in the approximation of "two sums over the wave vector." The results of this work can be applied for the numeric calculation of the heat capacity of liquid $^4$He in order to check the theoretical and experimental results quantatively, especially in the $\lambda$-transition region.