The self-consistent microscopic model of an energy spectrum of a superfluity $^{4}$He with the Hermitian form of Bogoliubov-Zubarev Hamiltonian

TL;DR

This paper introduces a self-consistent microscopic oscillator model for superfluid helium-4, providing new methods for calculating its energy spectrum, including anharmonic effects, decay processes, and condensate suppression, without adjustable parameters.

Contribution

It presents a novel Hermitian form of the Bogoliubov-Zubarev Hamiltonian and a self-consistent approach to determine the energy spectrum and condensate properties of superfluid helium-4.

Findings

Derived the dispersion curve considering decay processes.

Identified the endpoint of the dispersion curve related to roton decay.

Developed a parameter-free approach using the structure factor.

Abstract

Based on the collective variables representation with the Hermitian form of Bogoliubov-Zubarev Hamiltonian the self-consistent oscillator model of a ground state and excited states of Bose liquid has been proposed. The new method of calculation of anharmonic terms in this Hamiltonian and its interpretation have been presented. The dispersion equation for a collective excitation in a superfluid $^{4}$He has been obtained in self-consistent way, where real and virtual processes of decay of a collective excitation were considered. The end point, determined by a threshold of collective excitation's decay on two rotons, of the dispersion curve has been obtained and it was shown that the dispersion curve strongly depends on property of its stability. An approach with a structure factor has been realized without using of any adaption parameters. Based on the oscillator model the new method of self-consistent calculation of a ground state energy and density of Bose condensate has been proposed. The model of suppression of Bose condensate has been presented.