Excitation spectrum and mean energy of thermal fluctuations of a simple fluid in the Maxwell generalized hydrodynamics model
Phys. Rev. E 114, 044108 – Published 6 October, 2026
DOI: https://doi.org/10.1103/wstq-xr5d
Abstract
Within the framework of linear Maxwell generalized hydrodynamics, explicit expressions for the Green's functions of longitudinal and transverse modes are obtained. Using the fluctuation-dissipation theorem, the spectral densities of individual contributions to the total energy of the fluid are determined. Exact frequency integration by the residue method is performed for the kinetic and potential (elastic) energy. An explicit analytical expression for the total internal energy of the fluid as a function of the gap width in the wave-number spectrum of transverse modes is obtained. An expression for the excitation spectrum in the fluid is constructed. It is shown that the excitation spectrum in the Maxwell model does not generally have a Debye quadratic form. The results are placed in the context of the Maxwell-Frenkel theory of liquids, and comparison with existing numerical simulations is provided.
