Bose Liquid Mean-Field Theory with Application to HeI

A mean-field theory is developed for a Bose liquid enclosed in a large vessel 𝒱. In accord with liquid structure concepts of Mitus et al., the liquid in 𝒱 is assumed to consist of adjacent macroscopic subregions Λk. In each subregion the bosons perform a locally ordered motion with prevailing orientation k + x, which varies randomly when passing from one subregion to another. |k| is constant, whereas temperature dependence of |x| is governed by a mean-field theory (MFT). The theory is applied to simulate HeI heat capacity CV (T) at T > Tλ = 2.17 K and CV (T) singularity at [Formula: see text]. The MFT numerical heat capacity Cn(T) = ΔE/ΔT exhibits behaviour characteristic of a singularity at [Formula: see text]: rapid increase with decreasing ΔT. Apart from [Formula: see text], good agreement of Cn(T) with CV(T) experimental plot is also found above Tλ, at T ∊ (Tλ, 3K].

A Note on the Calculation of the Long-Wavelength Limit of the Bosonic Excitation Spectrum

An approach is proposed to analyse an interacting bosonic system using two-time temperature Green’s functions on the collective variables. Two systems are studied: liquid helium-4 and the Yukawa Bose liquid being a model of the nuclear matter. The suggested decoupling in the equations of motion for Green’s functions yields a good description of the elementary excitation spectrum in the long-wavelength limit.