arXiv subjects

Orest Hryhorchak

Publications and source records attributed to Orest Hryhorchak.

7 recordsLinked to original sources

arXiv2020

Large-$N$ expansion for condensation and stability of Bose-Bose mixtures at finite temperatures

The two-component mixture of Bose particles with short-range pairwise interaction at finite temperatures in three dimensions is considered. Particularly we examine, by means of the large-$N$ expansion technique, the stability of mixed state below the Bose-Einstein transition point and the temperature dependence of the condensate density for symmetric mixture of Bose gases. The presented analysis reveals the importance of finite-temperature excitations of the non-condensed particles in formation of the phase diagram of two-component Bose systems.

cond-mat.quant-gas↗

arXiv2020

Condensation and superfluidity of $SU(N)$ Bose gas

We perform the comprehensive comparison of properties of the condensate and superfluid densities for the $N$-component three-dimensional Bose gas with the symmetric inter- and intraspecies short-range interaction between particles. In particular, based on the large-$N$ expansion approach for many-boson systems we obtain general expression for density of the superfluid component that at very low temperatures reproduce the well-know Landau's formula and non-trivially includes the thermal fluctuations in the finite-temperature region, and compare it to the condensate density calculated previously. The numerically evaluated temperature dependencies are in a qualitatively good agreement with the results of Monte Carlo simulations.

cond-mat.quant-gas↗

arXiv2018

Large-$N$ properties of a non-ideal Bose gas

We rigorously discuss the large-$N$ thermodynamics of a Bose gas with a short-range two-body potential. Considering the system as a mixture of $N$ identical components with symmetrical interaction we calculated numerically the temperature dependence of the leading-order corrections to the depletion of Bose-Einstein condensate and to the isothermal compressibility.

cond-mat.quant-gas↗

arXiv2017

$1/N$-expansion for the critical temperature of the Bose gas

We revised the large-$N$ expansion for a three-dimensional Bose system with short-range repulsion in normal phase. Particularly, for the model potential that is characterised only by the $s$-wave scattering length $a$ the full numerical calculations of the critical temperature in the $1/N$-approximation as a function of the gas parameter $an^{1/3}$ are performed. Additionally to the well-known result in the dilute limit we estimated analytically the leading-order strong-coupling behavior of the Bose-Einstein condensation transition temperature. It is shown that the critical temperature shift of the non-ideal Bose gas grows at small $an^{1/3}$, reaches some maximal value and then falls down becoming negative.

cond-mat.quant-gas↗

arXiv2016

Effective mass of $^4$He atom in superfluid and normal phases

The formula for the temperature dependence of the effective mass of a $^{4}% $He atom in the superfluid and normal phases is obtained.\,\,This expression for the effective mass allows one to eliminate infra-red divergences, being applicable at all temperatures, except for a narrow fluctuation region 0.97~$\lesssim T/T_{\rm c}\leq1$.\,\,In the high and low temperature limits, as well as in the interactionless limit, the obtained expression reproduces the well known results.\,\,The temperature dependence of the heat capacity and the phase transition temperature $T_{\rm c}\approx$~2.18~K are calculated, by using the formula obtained for the effective mass.\,\,In the framework of the approach proposed in this work, the small critical index $η$ is determined in the random phase approximation.\,\,The obtained value corresponds to the well known result.

cond-mat.quant-gas↗

arXiv2016

Structure functions of many-boson system with regard for direct three- and four-particle correlations

On the basis of the expression for the density matrix of interacting Bose particles in the coordinate representation with regard for the direct three- and four-particle correlations [I.O.\,\,Vakarchuk and O.I.\,\,Hryhorchak, J.\,\,Phys.\,\,Stud.\,\,\textbf{3}, 3005 (2009)], the two-, three-, and four-particle structure factors of liquid $^{4}$He in a wide temperature interval were calculated in the approximation "one sum over the wave vector".\,\,In the low-temperature limit, the expression obtained for the two-particle structure factor transforms into the well-known one.\,\,In the high-temperature limit, the expressions for the two-, three-, and four-particle structure factors are reduced to those for the ideal Bose gas.\,\,The results obtained can be applied to calculations of the thermodynamic functions of liquid $^{4}$He and to the determination of the temperature dependence of the first-sound velocity in a many-boson system.

cond-mat.quant-gas↗

arXiv2015

Internal energy of many-boson system with three- and four-particle direct correlations taken into account

In this paper we calculate kinetic, potential and full energy with three- and four-particle direct correlations taken into account at wide temperature region on the base of the density matrix of the interacting Bose-particles [I. O. Vakarchuk, O. I. Hryhorchak, Journ. Phys. Stud. {\bf 3}, 3005 (2009)]. In the low temperature limit the obtained expression for the full energy is equal to the wellknown expression for ground state energy in the approximation of "two sums over the wave vector." The results of this work can be applied for the numeric calculation of the heat capacity of liquid $^4$He in order to check the theoretical and experimental results quantatively, especially in the $λ$-transition region.

cond-mat.quant-gas↗