arXiv subjects

Ivan Vakarchuk

Publications and source records attributed to Ivan Vakarchuk.

6 recordsLinked to original sources

arXiv2017

Impurity self-energy in the strongly-correlated Bose systems

We proposed the non-perturbative scheme for calculation of the impurity spectrum in the Bose system at zero temperature. The method is based on the path-integral formulation and describes an impurity as a zero-density ideal Fermi gas interacting with Bose system for which the action is written in terms of density fluctuations. On the example of the $^3$He atom immersed in the liquid helium-4 a good consistency with experimental data and results of Monte Carlo simulations is shown.

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↗

arXiv2007

Casimir effect in deformed field

The Casimir energy is calculated in one-, two-, and three-dimensional spaces for the field with generalized coordinates and momenta satisfying the deformed Poisson brackets leading to the minimal length.

quant-ph↗

arXiv2002

Schrodinger's cat and the problem of two cultures

A mathematical model of the interaction mechanism for the intuitive-imaginative and heuristic-logical thinking responsible for the rift in the intellectual activity into two cultures has been suggested. The said model proceeds from the assumption that human thinking is based on the principles of the many-channel quantum-mechanical logic of the "both ... and" type surpassing the rigid confines of the "either ... or" type classical logic. The aggregate product of the person equally endowed in the said two-cultural space has been calculated. The interferential part of the latter achieves its maximum at the extreme values of such parameters as the inter-state exchange frequency and the difference of the states phases.

quant-ph↗