4He spectrum shift caused by 3He admixture

Abstract

The shift ∆E of a maxon-roton 4 He excitation spectrum E via the 3 He admixture is considered theoretically. The Bogoliubov formula for E(ρ, g) as a function of Bose-condensate density ρ and of 4 He/ 4 He interaction g is used as an element of partition function formalism of the whole system, presented in the form of a path (functional) integral. The dependence of ρ on g, 4 He/ 3 He interaction λ as well as on the pressure P , induced by the 3 He admixture, is taken into account. The new model of g, suitable for analytical calculations, is used for a description of a change of P within the constant volume. The cases of positive and negative shifts are found as the result of competition between interactions g and λ.

4He spectrum shift caused by 3He admixture II

“…This is a continuation of the paper [1] over the same title. The main idea of these papers is to look for the theoretical key to understand the 4 He maxon-roton excitation curve shift, caused by 3 He admixture.…”

“…The main idea of these papers is to look for the theoretical key to understand the 4 He maxon-roton excitation curve shift, caused by 3 He admixture. The sections 1-4 of [1] are shortly repeated here in the sections 2-3. The phenomenological interpretation of section 5 in [1] is replaced by a new theoretical investigation, represented in the sections 4,5,6 of the present paper.…”

“…The sections 1-4 of [1] are shortly repeated here in the sections 2-3. The phenomenological interpretation of section 5 in [1] is replaced by a new theoretical investigation, represented in the sections 4,5,6 of the present paper. This investigation classifies the types of dispersion shifts as a result of competition between the 4 He/ 3 He and 4 He/ 4 He interactions, accompanying by effects of pressure, induced by the 3 He admixture in the V = const volume.…”

“…Note, that all the terms of the partition function(6) are taken into account in(7) regardless their dependence (or not) on the boson variables. It was not so with the formula (18) in[1], where some terms were illegally omitted.…”