Phonon and optical-roton branches of excitations of the Bose system

TL;DR

This paper derives a model for Bose systems revealing two excitation branches, including a phonon and an optical branch with a gap, and discusses their properties at various densities, relating findings to superfluid helium-4.

Contribution

It introduces a coupled equations framework for Bose excitations, accounting for finite interaction range, and predicts a dual-branch spectrum with roton-like features.

Findings

Identification of two excitation branches: phonon and optical with an energy gap.

Both branches exhibit nonmonotonic behavior with roton-like minima at high density.

Analysis aligns with neutron scattering experiments on superfluid He-4.

Abstract

For a system of a large number of Bose particles, a chain of coupled equations for the averages of field operators is obtained. In the approximation where only the averages of one field operator and the averages of products of two operators at zero temperature are taken into account, there is derived a closed system of dynamic equations. Taking into account the finite range of the interaction potential between particles, the spectrum of elementary excitations of a many-particle Bose system is calculated, and it is shown that it has two branches: a sound branch and an optical branch with an energy gap at zero momentum. At high density, both branches are nonmonotonic and have the roton-like minima. The dispersion of the phonon part of the spectrum is considered. The performed calculations and analysis of experiments on neutron scattering allow to make a statement about the complex structure of the Landau dispersion curve in the superfluid He-4.