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 TMF, 1980, Volume 42, Number 1, Pages 112–123 (Mi tmf3727)

Microscopic theory of the energy spectrum of liquid HeII

I. A. Vakarchuk, I. R. Yukhnovskii

Abstract: The wave function $\psi_k$ of the lowest excites state of many-boson system is represented as the product of the wave function of the ground state $\psi_0=e^U$ and the function $\varphi_k$ which takes into account the existence of the excitation with the momentum $\hbar k$ and the energy $E(k)$. The function $U$ and $\varphi_k$ are represented as the series over the collective variables which are the Fourier coefficients of the operator of density fluctuations. The systems of coupled equations for the coefficient functions of these series are derived. The system of two integral equations connecting the excitation spectrum $E(k)$ with the structure factor of the system is obtained by means of breaking the chain of equations. This makes it possible to apply the results obtained to the liquid $\mathrm{He}^4$. The damping of the spectrum is described. It is shown that the expansion of the spectrum in the limit of small momentum $\hbar k$ includes the odd powers of $\hbar k$ only.

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English version:
Theoretical and Mathematical Physics, 1980, 42:1, 73–80

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Citation: I. A. Vakarchuk, I. R. Yukhnovskii, “Microscopic theory of the energy spectrum of liquid HeII”, TMF, 42:1 (1980), 112–123; Theoret. and Math. Phys., 42:1 (1980), 73–80

Citation in format AMSBIB
\Bibitem{VakYuk80} \by I.~A.~Vakarchuk, I.~R.~Yukhnovskii \paper Microscopic theory of the energy spectrum of liquid HeII \jour TMF \yr 1980 \vol 42 \issue 1 \pages 112--123 \mathnet{http://mi.mathnet.ru/tmf3727} \transl \jour Theoret. and Math. Phys. \yr 1980 \vol 42 \issue 1 \pages 73--80 \crossref{https://doi.org/10.1007/BF01019263} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1980KA96200012} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. V. A. Onischuk, “Collective variables. Correlation functions on Gaussian functionals”, Theoret. and Math. Phys., 51:3 (1982), 582–593
2. G. O. Balabanyan, “Construction of theory of a binary mixture of nonideal Bose gases (or liquids) by the method of collective variables I. Wave function and ground-state energy, excitation spectrum, correlation functions, thermodynamics of the system at $T=0$”, Theoret. and Math. Phys., 66:1 (1986), 81–97
3. I. A. Vakarchuk, P. A. Glushak, “Free energy of a many-boson system at low temperatures”, Theoret. and Math. Phys., 75:1 (1988), 399–408
4. Vakarchuk I.O. Pastukhov V.S. Prytula R.O., “Theory of Structure and Thermodynamic Function of Liquid He-4 (Review Article)”, Low Temp. Phys., 39:9 (2013), 741–751
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