arXiv subjects

Yu. A. Mishchenko

Publications and source records attributed to Yu. A. Mishchenko.

12 recordsLinked to original sources

arXiv2025

The $μ$-deformed Einstein field equations with $μ$-dependent effective cosmological constant

In this paper, we derive the $μ$-deformed Einstein field equations from the generalized thermodynamic functions of the $μ$-deformed analog of Bose gas model, applying the (adapted) Verlinde's approach. The basic role of deformation parameter is shown: it provides the possibility to vary the value of the cosmological constant. Due to this, we suggest an interesting treatment of the cosmological constant (CC) problem within the framework of $μ$-deformation. Namely, viewing the derived $μ$-deformed CC as an effective one and varying the parameter $μ$ appropriately, we gain the possibility to drastically reduce the CC, so as to get for it the realistic value. The relation to dark matter is of importance.

gr-qc↗

arXiv2019

Composite Fermions as Deformed Oscillators: Wavefunctions and Entanglement

Composite structure of particles somewhat modifies their statistics, compared to the pure Bose- or Fermi-ones. The spin-statistics theorem, so, is not valid anymore. Say, $π$-mesons, excitons, Cooper pairs are not ideal bosons, and, likewise, baryons are not pure fermions. In our preceding papers, we studied bipartite composite boson (i.e. quasiboson) systems via a realization by deformed oscillators. Therein, the interconstituent entanglement characteristics such as entanglement entropy and purity were found in terms of the parameter of deformation. Herein, we perform an analogous study of composite Fermi-type particles, and explore them in two major cases: (i) "boson + fermion" composite fermions (or cofermions, or CFs); (ii) "deformed boson + fermion" CFs. As we show, cofermions in both cases admit only the realization by ordinary fermions. Case (i) is solved explicitly, and admissible wavefunctions are found along with entanglement measures. Case (ii) is treated within few modes both for CFs and constituents. The entanglement entropy and purity of CFs are obtained via the relevant parameters and illustrated graphically.

quant-ph↗

arXiv2015

Correlation function intercepts for $\tildeμ,q$-deformed Bose gas model implying effective accounting for interaction and compositeness of particles

In the recently proposed two-parameter $\tildeμ,q$-deformed Bose gas model [Ukr. J. Phys. {\bf 58}, 1171 (2013), arXiv:1312.1573] aimed to take effectively into account both compositeness of particles and their interaction, the $\tildeμ,q$-deformed virial expansion of the equation of state (EOS) was obtained. In this paper we further explore the $\tildeμ,q$-deformation, namely the version of $\tildeμ,q$-Bose gas model involving deformed distributions and correlation functions. In the model, we explicitly derive the one- and two-particle deformed distribution functions and the intercept of two-particle momentum correlation function. The results are illustrated by plots, and the comparison with known experimental data on two-pion correlation function intercepts extracted in RHIC/STAR experiments is given.

hep-ph↗

arXiv2015

Entanglement entropy of composite fermions realized by (deformed) fermions vs. that of composite bosons

In our two preceding papers we studied bipartite composite boson (or quasiboson) systems through their realization in terms of deformed oscillators. Therein, the entanglement characteristics such as the entanglement entropy and purity were found and expressed, for both one-quasiboson and more complex states, through the parameter of deformation. In this work we initiate an analogous study of composite fermions for two major cases: (i) "boson + fermion" composites; (ii) "deformed-boson + fermion" composites. Both the entanglement entropy and purity of composite fermions are dealt with, their dependence on the relevant parameters established, and for some particular two- or three-mode cases depicted graphically. In a few special cases the entanglement entropy turns out to be constant $S_0=\ln 2$ (or $\ln 3$) or $S_0=0$, while in the rest of the cases which we considered it varies between zero and $\ln 2$ (or $\ln 3$).

quant-ph↗

arXiv2014

Virial coefficients in $(\tildeμ,q)$-Bose gas model related to compositeness of particles and their interaction: temperature-dependence problem

We establish the relation of the second virial coefficient of certain $(\tildeμ,q)$-deformed Bose gas model, recently proposed by the authors in [Ukr. J. Phys., 2013], to the interaction and compositeness parameters when either of these factors is taken into account separately. When the interaction is dealt with, the deformation parameter becomes linked directly to the scattering length, and the effective radius of interaction (in general, to scattering phases). The additionally arising temperature dependence is a new feature absent in the deformed Bose gas model within adopted interpretation of the deformation parameters $\tildeμ$ and $q$. Here the problem of the temperature dependence is analyzed in detail and its possible solution is proposed.

cond-mat.stat-mech↗

arXiv2014

Multiparticle distributions and intercepts of $r$-particle correlation functions in the symmetric Tamm-Dancoff type $q$-Bose gas model

Symmetric Tamm-Dancoff (STD) type $q$-deformed quantum oscillators are used as the base for constructing the respective STD type $q$-Bose gas model. In this letter, within the STD $q$-deformed Bose gas model we derive explicit analytic expressions for the $r$-particle momentum distribution functions, and for the (momentum) correlation function intercepts of 2nd, 3rd, and any $r$th order. Besides, we obtain large-momentum asymptotic formulas for the $r$th order intercepts which show dependence on the $q$-parameter only. The obtained formulas provide new example, in addition to already known two cases, of exact results for $r$-particle distributions and the correlation function intercepts in deformed analogs of Bose gas model.

quant-ph↗

arXiv2013

Deformed Bose gas models aimed at taking into account both compositeness of particles and their interaction

We consider the deformed Bose gas model with the deformation structure function that is the combination of a q-deformation and a quadratically polynomial deformation. Such a choice of the unifying deformation structure function enables us to describe the interacting gas of composite (two-fermionic or two-bosonic) bosons. Using the relevant generalization of the Jackson derivative, we derive a two-parametric expression for the total number of particles, from which the deformed virial expansion of the equation of state is obtained. The latter is interpreted as the virial expansion for the effective description of a gas of interacting composite bosons with some interaction potential.

math-ph↗

arXiv2013

Energy dependence of the entanglement entropy of composite boson (quasiboson) systems

Bipartite composite boson (quasiboson) systems, which admit realization in terms of deformed oscillators, were considered in our previous paper from the viewpoint of entanglement characteristics. These characteristics, including entanglement entropy and purity, were expressed through the relevant deformation parameter for different quasibosonic states. On the other hand, it is of interest to present the entanglement entropy and likewise the purity as function of energy for those states. In this work, the corresponding dependencies are found for different states of composite bosons realized by deformed oscillators and, for comparison, also for the hydrogen atom viewed as composite boson. The obtained results are expressed graphically and their implications discussed.

quant-ph↗

arXiv2012

Exact expressions for the intercepts of r-particle momentum correlation functions in μ-Bose gas model

Recently, the deformed μ-Bose gas model based on so called μ-deformed oscillators was proposed. For that model, the intercepts of r-particle momentum correlation functions (correlation functions at coinciding momenta of particles) were treated for r=2,3, within certain order of approximation in μ. In this work, we derive for μ-Bose gas model the {\it exact} expressions for r-particle correlation function intercepts, for all r, through Lerch transcendent and find their asymptotics (as functions of μ). For 2-, 3-particle intercepts and deformed distribution function the dependence on particles momentum is presented graphically.

math-ph↗

arXiv2011

Entanglement in composite bosons realized by deformed oscillators

Composite bosons (or quasibosons), as recently proven, are realizable by deformed oscillators and due to that can be effectively treated as particles of nonstandard statistics (deformed bosons). This enables us to study quasiboson states and their inter-component entanglement aspects using the well developed formalism of deformed oscillators. We prove that the internal entanglement characteristics for single two-component quasiboson are determined completely by the parameter(s) of deformation. The bipartite entanglement characteristics are generalized and calculated for arbitrary multi-quasiboson (Fock, coherent etc.) states and expressed through deformation parameter.

quant-ph↗

arXiv2011

Quasibosons composed of two q-fermions: realization by deformed oscillators

Composite bosons, here called {\it quasibosons} (e.g. mesons, excitons, etc.), occur in various physical situations. Quasibosons differ from bosons or fermions as their creation and annihilation operators obey non-standard commutation relations, even for the "fermion+fermion" composites. Our aim is to realize the operator algebra of quasibosons composed of two fermions or two q-fermions (q-deformed fermions) by the respective operators of deformed oscillators, the widely studied objects. For this, the restrictions on quasiboson creation/annihilation operators and on the deformed oscillator (deformed boson) algebra are obtained. Their resolving proves uniqueness of the family of deformations and gives explicitly the deformation structure function (DSF) which provides the desired realization. In case of two fermions as constituents, such realization is achieved when the DSF is quadratic polynomial in the number operator. In the case of two q-fermions, q\neq 1, the obtained DSF inherits the parameter q and does not continuously converge when q\to 1 to the DSF of the first case.

math-ph↗

arXiv2011

Two-fermion composite quasi-bosons and deformed oscillators

The concept of quasi-bosons or composite bosons (like mesons, excitons etc.) has a wide range of potential physical applications. Even composed of two pure fermions, the quasi-boson creation and annihilation operators satisfy non-standard commutation relations. It is natural to try to realize the quasi-boson operators by the operators of deformed (nonlinear) oscillator, the latter constituting widely studied field of modern quantum physics. In this paper, it is proved that the deformed oscillators which realize quasi-boson operators in a consistent way really exist. The conditions for such realization are derived, and the uniqueness of the family of deformations under consideration is shown.

quant-ph↗