arXiv subjects

I. I. Kachurik

Publications and source records attributed to I. I. Kachurik.

17 recordsLinked to original sources

arXiv2023

New Deformed Heisenberg Algebra from the $μ$-Deformed Model of Dark Matter

Recently, the $μ$-deformation-based approach to modeling dark matter, which exploits $μ$-deformed thermodynamics, was extended to the study of galaxy halo density profile and of the rotation curves of a number of (dwarf or low brightness) galaxies. For that goal, $μ$-deformed analogs of the Lane--Emden equation (LEE) have been proposed, and their solutions describing density profiles obtained. There are two seemingly different versions of $μ$-deformed LEE which possess the same solution, and so we deal with their equivalence. From the latter property we derive new, rather unusual, $μ$-deformed Heisenberg algebra (HA) for the position and momentum operators, and present the $μ$-HA in few possible forms (each one at $μ\to0$ recovers usual HA). The generalized uncertainty relation linked with the new $μ$-HA is studied, along with its interesting implications including the appearance of the quadruple of both maximal and minimal lengths and momenta.

astro-ph.GA↗

arXiv2019

Galaxy rotation curves in the $μ$-deformation based approach to dark matter

We elaborate further the $μ$-deformation-based approach to modeling dark matter, in addition to the earlier proposed use of $μ$-deformed thermodynamics. Herein, we construct $μ$-deformed analogs of the Lane-Emden equation (for density profiles), and find their solutions. Using these, we plot the rotation curves for a number of galaxies. Different curves describing chosen galaxies are labeled by respective (differing) values of the deformation parameter $μ$. As result, the use of $μ$-deformation leads to improved agreement with observational data. For all the considered galaxies, the obtained rotation curves (labeled by $μ$) agree better with data as compared to the well known Bose-Einstein condensate model results of T.Harko. Besides, for five of the eight cases of galaxies we find better picture for rotation curves than the corresponding Navarro-Frenk-White (NFW) curves. Possible physical meaning of the parameter $μ$, basic for this version of $μ$-deformation, is briefly discussed.

physics.gen-ph↗

arXiv2018

Pseudo-Hermitian position and momentum operators, Hermitian Hamiltonian, and deformed oscillators

The recently introduced by us two- and three-parameter ($p,q$)- and ($p,q,μ$)-deformed extensions of the Heisenberg algebra were explored under the condition of their direct link with the respective (nonstandard) deformed quantum oscillator algebras. In this paper we explore certain Hermitian Hamiltonian build in terms of non-Hermitian position and momentum operators obeying definite $η(N)$-pseudo-Hermiticity properties. A generalized nonlinear (with the coefficients depending on the excitation number operator $N$) one-mode Bogolyubov transformation is developed as main tool for the corresponding study. Its application enables to obtain the spectrum of "almost free" (but essentially nonlinear) Hamiltonian.

quant-ph↗

arXiv2018

Condensate of $μ$-Bose gas as a model of dark matter

Though very popular, Bose-Einstein condensate models of dark matter have some difficulties. Here we propose the so-called $μ$-Bose gas model ($μ$-BGM) as a model of dark matter, able to treat weak points. Within $μ$-BGM, the $μ$-dependence of thermodynamics arises through the respective $μ$-calculus (it generalizes usual differential calculus) and enters the partition function, total number of particles, internal energy, etc. We study thermodynamic geometry of the $μ$-BGM and find singular behavior of (scalar) curvature, confirming Bose-like condensation. The critical temperature of condensation $T^{(μ)}_c$ for $μ\neq 0$ is higher than the boson $T_c$. We find other important virtues of $μ$-thermodynamics versus usual bosons and conclude: the condensate of $μ$-Bose gas can serve as (an effective) model of galactic-halos dark matter.

gr-qc↗

arXiv2017

The use of $μ$-Bose gas model for effective modeling of dark matter

For the recently introduced $μ$-deformed analog of Bose gas model ($μ$-Bose gas model), its thermodynamical aspects e.g. total number of particles and the partition function are certain functions of the parameter $μ$. This basic $μ$-dependence of thermodynamics of the $μ$-Bose gas arises through the so-called $μ$-calculus, an alternative to the known $q$-calculus (Jackson derivative, etc.), so we include main elements of $μ$-calculus. Likewise, virial expansion of EOS and virial coefficients, the internal energy, specific heat and the entropy of $μ$-Bose gas show $μ$-dependence. Herein, we study thermodynamical geometry of $μ$-Bose gas model and find the singular behavior of (scalar) curvature, signaling for Bose-like condensation. The critical temperature of condensation $T^{(μ)}_c$ depending on $μ$ is given and compared with the usual $T_c$, and with known $T_c^{(p,q)}$ of $p,q$-Bose gas model. Using the results on $μ$-thermodynamics we argue that the condensate of $μ$-Bose gas, like the earlier proposed infinite statistics system of particles, can serve for effective modeling of dark matter.

cond-mat.stat-mech↗

arXiv2016

New version of pseudo-hermiticity in the two-sided deformation of Heisenberg algebra

The recently introduced two- and three-parameter ($p,q$)- and ($p,q,μ$)-deformed extensions of the Heisenberg algebra were explored under the condition of their connectedness with the respective nonstandard (other than known ones) deformed quantum oscillator algebras. In this paper we show that such connection dictates certain new $η(N)$-pseudo-Hermitian conjugation rule between the creation and annihilation operators, with $η(N)$ depending on the particle number operator $N$. In turn, that leads to the related $η(N)$-pseudo-Hermiticity of the position/momentum operators, though the involved Hamiltonian is Hermitian. Different possible cases are studied, and some interesting features implied by the use of such $η(N)$-based conjugation rule are emphasized.

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

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↗

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↗

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↗

arXiv2010

Quasi-Fibonacci oscillators

We study the properties of sequences of the energy eigenvalues for some generalizations of q-deformed oscillators including the p,q-oscillator, the 3-, 4- and 5-parameter deformed oscillators given in the literature. It is shown that most of the considered models belong to the class of so-called Fibonacci oscillators for which any three consequtive energy levels satisfy the relation E_{n+1}=λE_n+ρE_{n-1} with real constants λ, ρ. On the other hand, for certain μ-oscillator known from 1993 we prove the fact of its non-Fibonacci nature. Possible generalizations of the three-term Fibonacci relation are discussed among which we choose, as most adequate for the μ$-oscillator, the so-called quasi-Fibonacci (or local Fibonacci) property of the energy levels. The property is encoded in the three-term quasi-Fibonacci (QF) relation with non-constant, n-dependent coefficients λand ρ. Various aspects of the QF relation are elaborated for the μ-oscillator and some of its extensions.

quant-ph↗

arXiv2004

Baryon Decuplet Masses From the Viewpoint of q-Equidistance

Masses of baryons {3/2}^+ are calculated on the base of representations of dynamical "pseudounitary" q-deformed algebra u(4,1)_q which provides necessary breaking of the 4-flavor symmetry realized by the assumed q-algebra su(4)_q. It is demonstrated that, contrary to the case of su(3)_q octet baryons {1/2}^+, one and the same q-analog of mass relation for baryons {3/2}^+ from decuplet embedded into 20-plet of su(4)_q follows from evaluations within all the different admissible "dynamical" representations.

hep-ph↗

arXiv2003

Linking the parameters of diquark-quark model to the Cabibbo angle

From two different modifications of the Gell-Mann-Okubo mass relation for (1/2)^+ baryons: the first one given by a version of diquark-quark model and the second one being the optimal mass sum rule obtained by using quantum groups U_q(su_n) for the role of hadronic flavor symmetries, we find direct connection of the mass parameters of the diquark-quark model of Lichtenberg, Tassie and Keleman to the (proper value of) q-parameter and then to the Cabibbo angle.

hep-ph↗

arXiv1995

Representations of the $U_q(u_{4,1})$ and a $q$-polynomial that determines baryon mass sum rules

With quantum groups $U_q(su_n)$ taken as classifying symmetries for hadrons of $n$ flavors, we calculate within irreducible representation $D^+_{12}(p-1,p-3,p-4;p,p-2)$ ($p \in {\bf Z}$) of 'dynamical' quantum group $U_q(u_{4,1})$ the masses of baryons ${1\over 2}^+$ that belong to ${\it 20}$-plet of $U_q(su_4)$. The obtained $q$-analog of mass relation (MR) for $U_q(su_3)$-octet contains unexpected mass-dependent term multiplied by the factor ${A_q\over B_q}$ where $A_q,$ $B_q$ are certain polynomials (resp. of 7-th and 6-th order) in the variable $q+q^{-1}\equiv [2]_q$. Both values $q=1$ and $q=e^{iπ\over 6}$ turn the polynomial $A_q$ into zero. But, while $q=1$ results in well-known Gell-Mann--Okubo (GMO) baryon MR, the second root of $A_q$ reduces the $q$-MR to some novel mass sum rule which has irrational coefficients and which holds, for empirical masses, even with better accuracy than GMO mass sum rule.

hep-ph↗