Phonon and Optical-roton Branches of Excitations of the Bose System

• Published in: Journal of low temperature physics Vol. 210; no. 1-2; pp. 68 - 92
• Main Authors: Poluektov, Yu. M., Soroka, A. A.
• Format: Journal Article
• Language: English
• Published: New York Springer US 2023; Springer Nature B.V
• Subjects: Characterization and Evaluation of Materials; Condensed Matter Physics; Dispersion curve analysis; Elementary excitations; Energy gap; Excitation spectra; Fluids; Low temperature physics; Magnetic Materials; Magnetism; Mathematical analysis; Neutron scattering; Operators; Phonons; Physics; Physics and Astronomy; Superfluidity; Bose–Einstein condensate; Sound excitations; Excitations with energy gap; Superfluidity; Pair correlations; Anomalous and normal averages
• ISSN: 0022-2291; 1573-7357
• DOI: 10.1007/s10909-022-02885-8

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 4 He.