arXiv subjects

A. M. Gavrilik

Publications and source records attributed to A. M. Gavrilik.

At least 37 records · Page 2Linked to original sources

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↗

arXiv2014

Symmetric Tamm-Dancoff q-oscillator: representation, quasi-Fibonacci nature, accidental degeneracy and coherent states

In this paper we propose a symmetric q-deformed Tamm-Dancoff (S-TD) oscillator algebra and study its representation, coordinate realization, and main properties. In particular, the non-Fibonacci (more exactly, quasi-Fibonacci) nature of S-TD oscillator is established, the possibility of relating it to certain p,q-deformed oscillator family shown, the occurrence of the pairwise accidental degeneracy proven. We also find the coherent state for the S-TD oscillator and show that it satisfies completeness relation. Main advantage of the S-TD model over usual Tamm-Dancoff oscillator is that due to (q<-->q^{-1})- symmetry it admits not only real, but also complex (phase-like) values of the deformation parameter q.

math-ph↗

arXiv2014

Elements of $μ$-calculus and thermodynamics of $μ$-Bose gas model

We review on and give some further details about the thermodynamical properties of the μ-Bose gas model (arXiv:1309.1363) introduced by us recently. This model was elaborated in connection with μ-deformed oscillators. Here, we present the necessary concepts and tools from the so-called μ-calculus. For the high temperatures, we obtain the virial expansion of the equation of state, as well as five virial coefficients. In the regime of low temperatures, the critical temperature of condensation is inferred. We also obtain the specific heat, internal energy, and entropy for a μ-Bose gas for both low and high temperatures. All thermodynamical functions depend on the deformation parameter μ. The dependences of the entropy and the specific heat on the deformation parameter are visualized.

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

New version of $q$-deformed supersymmetric quantum mechanics

A new version of the q-deformed supersymmetric quantum mechanics (q-SQM), which is inspired by the Tamm--Dankoff-type (TD-type) deformation of quantum harmonic oscillator, is constructed. The obtained algebra of q-SQM is similar to that in Spiridonov's approach. However, within our version of q-SQM, the ground state found explicitly in the special case of superpotential yiealding q-superoscillator turns out to be non-Gaussian and takes the form of special (TD-type) q-deformed Gaussian.

quant-ph↗

arXiv2013

Thermostatistics of μ-deformed analog of Bose gas model

For the recently introduced μ-deformed analog of Bose gas model (μ-Bose gas model) we study some thermodynamical aspects. Namely, we calculate total number of particles and, from it, the deformed partition function, both involving dependence on the deformation parameter μ. Such dependence of thermodynamic functions on the μ-parameter is at the core of modification of Bose gas model and arises through the use of new techniques given by us, the μ-calculus, an alternative to the well-known q-calculus (Jackson derivative and integral). Necessary elements of μ-calculus are first presented. Then, for high temperatures we obtain virial expansion of the equation of state and find five first virial coefficients, as functions of μ. At the other end, for low temperatures the critical temperature of condensation T_c^(μ) depending on μis found and compared with the usual T_c, and with the T_c^(p,q) of earlier studied p,q-Bose gas model. The internal energy, specific heat and the entropy of μ-Bose gas are also given, both for high and low temperatures. Features peculiar for the μ-Bose gas model are emphasized.

cond-mat.stat-mech↗

arXiv2013

Plethora of q-oscillators possessing pairwise energy level degeneracy

Using the q,p-deformed oscillators as basic generating system, we obtain diverse classes (which form distinct sectors of functional continua) of novel versions of q-deformed oscillators, all of which share the property of "accidental" degeneracy within a fixed pair of energy levels E_{m} = E_{m+1}, m\ge 1, occurring at the real deformation parameter fixed by an appropriate value q(m) that depends on m and on particular model. Likewise, the degeneracy E_{0} = E_{k} (where k\ge 2) takes place, for properly fixed q=q(k), in most of those models. The formerly studied model of q-oscillator known as the Tamm-Dancoff cutoff deformed oscillator is contained in the continua as isolated special case.

quant-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↗

arXiv2012

Three-parameter (two-sided) deformation of Heisenberg algebra

A 3-parametric two-sided deformation of Heisenberg algebra (HA), with p,q-deformed commutator in the l.h.s. of basic defining relation and certain deformation of its r.h.s., is introduced and studied. The third deformation parameter μappears in an extra term in the r.h.s. as pre-factor of Hamiltonian. For this deformation of HA we find novel properties. Namely, we prove it is possible to realize this (p,q,μ)-deformed HA by means of some deformed oscillator algebra. Also, we find the unusual property that the deforming factor μ in the considered deformed HA inevitably depends explicitly on particle number operator N. Such a novel N-dependence is special for the two-sided deformation of HA treated jointly with its deformed oscillator realizations.

math-ph↗

arXiv2012

Deformed gas of p,q-bosons: virial expansion and virial coefficients

In the study of many-particle systems both the interaction of particles can be essential and such feature as their internal (composite) structure. To describe these aspects, the theory of deformed oscillators is very efficient. Viewing the particles as p,q-deformed bosons, in the corresponding p,q-Bose gas model we obtain in explicit form virial expansion along with the 2nd to 5th virial coefficients. The obtained virial coefficients depend on the deformation parameters p,q in the form symmetric under p<->q, and at p->1, q->1 turn into those known for usual bosons. Besides real parameters, we analyze the case of complex mutually conjugate p and q and find interesting implications. Also, the critical temperature is derived (for the p,q-Bose gas) and compared with the T_c of standard case of Bose condensation. Similar results are presented for the deformed Bose gas model of the Tamm-Dancoff type.

cond-mat.stat-mech↗

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↗

arXiv2011

Alexander Polynomial Invariants of Torus Knots T(n,3) and Chebyshev Polynomials

The explicit formula, which expresses the Alexander polynomials Δ_{n,3}(t) of torus knots T(n,3) as a sum of the Alexander polynomials Δ_{k,2}(t) of torus knots T(k,2), is found. Using this result and those from our previous papers, we express the Alexander polynomials Δ_{n,3}(t) through Chebyshev polynomials. The latter result is extended to general torus knots T(n,l) with n and l coprime.

math-ph↗