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I. O. Vakarchuk

Publications and source records attributed to I. O. Vakarchuk.

13 recordsLinked to original sources
arXiv2015

Theory of a many-boson system with deformed Heisenberg algebra

We propose to consider nonlinear fluctuations in the theory of liquid $^{4}$He deforming the commutation relations between the generalized coordinates and momenta. Generalized coordinates are coefficients of density fluctuations of Bose particles. The deformation parameter takes into account the effects of three- and four-particle correlations in the behavior of a system. This parameter is defined from the experimental values of the elementary excitation spectrum and the structure factor extrapolated to $T=0$ K. The numerical estimation of the ground state energy and the Bose condensate fraction is made. The elementary excitation spectrum and the potential of interaction between the helium atoms are recovered.

cond-mat.quant-gas↗
arXiv2011

Microscopic theory of heat capacity of liquid helium-4 for temperatures above the critical point

In this paper, with the corresponding formula for internal energy obtained in Ref. [J. Phys. Stud. {\bf 11}, 259 (2007)], combined with a simple calculation of the effective mass of interacting Bose particles, the behavior of the heat capacity of liquid $^4$He is analyzed numerically for the entire temperature range. The results agree quite well with experimental data.

cond-mat.quant-gas↗
arXiv2006

One dimensional Coulomb-like problem in deformed space with minimal length

Spectrum and eigenfunctions in the momentum representation for 1D Coulomb potential with deformed Heisenberg algebra leading to minimal length are found exactly. It is shown that correction due to the deformation is proportional to square root of the deformation parameter. We obtain the same spectrum using Bohr-Sommerfeld quantization condition.

quant-ph↗
arXiv2005

WKB approximation in deformed space with minimal length

The WKB approximation for deformed space with minimal length is considered. The Bohr-Sommerfeld quantization rule is obtained. A new interesting feature in presence of deformation is that the WKB approximation is valid for intermediate quantum numbers and can be invalid for small as well as very large quantum numbers. The correctness of the rule is verified by comparing obtained results with exact expressions for corresponding spectra.

quant-ph↗
arXiv2005

On Dirac theory in the space with deformed Heisenberg algebra. Exact solutions

The Dirac equation has been studied in which the Dirac matrices $\hat{\boldmath$α$}, \hatβ$ have space factors, respectively $f$ and $f_1$, dependent on the particle's space coordinates. The $f$ function deforms Heisenberg algebra for the coordinates and momenta operators, the function $f_1$ being treated as a dependence of the particle mass on its position. The properties of these functions in the transition to the Schrödinger equation are discussed. The exact solution of the Dirac equation for the particle motion in the Coulomnb field with a linear dependence of the $f$ function on the distance $r$ to the force centre and the inverse dependence on $r$ for the $f_1$ function has been found.

quant-ph↗
arXiv2005

A self-consistent theory of liquid He-4

A new method is proposed for the calculation of full density matrix and thermodynamic functions of a many-boson system. Explicit expressions are obtained in the pair correlations approximation for an arbitrary temperature. The theory is self-consistent in the sence that the calculated properties at low temperatures coincide with that of Bogoliubov theory and in the high-temperature limit lead to the results for classical non-ideal gas in the random phase approximation. The phase transition is also revealed as a concequence of Bose-Einstein condensation deformed by interatomic interactions. All the final formulae are written solely via the liquid structure factor taken as a source information instead of the interatomic potential and, therefore, interconnect only observable quantities. This gives also a possibility to study such a strongly non-ideal system as liquid He-4.

quant-ph↗
arXiv2005

Kepler problem in Dirac theory for a particle with position-dependent mass

Exact solution of Dirac equation for a particle whose potential energy and mass are inversely proportional to the distance from the force centre has been found. The bound states exist provided the length scale $a$ which appears in the expression for the mass is smaller than the classical electron radius $e^2/mc^2$. Furthermore, bound states also exist for negative values of $a$ even in the absence of the Coulomb interaction. Quasirelativistic expansion of the energy has been carried out, and a modified expression for the fine structure of energy levels has been obtained. The problem of kinetic energy operator in the Schrödinger equation is discussed for the case of position-dependent mass. In particular, we have found that for highly excited states the mutual ordering of the inverse mass and momentum operator in the non-relativistic theory is not important.

quant-ph↗
arXiv2001

Calculation of the Condensate Fraction in Liquid Helium-4

We adduce the results of the condensate fraction calculation for liquid helium-4. The method is derived from the first principles and involves minimum assumptions. The only experimental quantity we need in our calculations is the static structure factor which is easily measurable. We use the approximation in which expressions contain one summation in the wave vector space (or one integration it the radius vector space) in order to demonstrate the validity of our method. The computed values of the condensate fraction lie within $8.8 ÷14%$ depending on the model potential for the short-range interaction. This result agrees with recent experimental measurements and numerical estimations.

cond-mat.stat-mech↗
arXiv2001

Thermodynamics of the Bose-System with a Small Number of Particles

A theoretical description of the interacting Bose-system is proposed. It is based on the extrapolation of the results obtained for the systems with a small number of particles N=2, 3, 4, etc. to the bulk case of N=\infty. It is shown that already the system with N=12, 13 behaves almost as a bulk in a wide temperature range. Special attention is paid to the phase transition in these systems. The hard sphere potential is used in calculations. The sequence of heat capacity maxima is approximated as C^{max}_N/N\simeq13.6-aN^{-ε} with ε=0.0608 giving the value of bulk heat capacity as 13.6 while experimental value is close to 16. The temperature of λ-transition is estimated as 2.1-2.3 K versus experimental 2.17 K. Quite good qualitative and satisfactory quantitative agreement with the experimental data has been achieved.

cond-mat.stat-mech↗
arXiv2001

Representation of the Short-Range Interactions in Liquid Helium via Modified Hard Sphere Potentials

In this paper we propose five different modifications of the hard sphere potential for the modeling a short-range repulsion and the calculation of thermodynamic and transport properties of liquid He4. We calculate the potential energy, the total energy, and the sound velocity at T=0 K. It is shown that three of the proposed potentials give a satisfactory description of these properties.

cond-mat.stat-mech↗
arXiv1998

Impurity effective mass in superfluid $^4$He

The system of bose liquid + impurity is considered. The energy spectrum as well as effective mass of impurity is calculated. For the case of the $ ^3He$ atom in superfluid $^4He$ numerical calculations are performed.

cond-mat↗