arXiv subjects

A. M. Gavrilik

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

At least 55 records · Page 3Linked to original sources

arXiv2011

Intercepts of the momentum correlation functions in μ-Bose gas model and their asymptotics

The so-called μ-deformed oscillator (or μ-oscillator) introduced by A.Jannussis, though possesses rather exotic properties with respect to other better known deformed oscillator models, also has good potential for diverse physical applications. In this paper, the corresponding μ-Bose gas model based on μ-oscillators is explored. Within this model, the intercepts λ^(2)(K) and λ^(3)(K) of two- and three-particle momentum correlation functions are calculated with the goal of possible application for modeling the non-Bose type behavior of the intercepts of two- and three-pion correlations, observed in the experiments on relativistic heavy ion collisions. In derivation of intercepts, different orders of approximation in the deformation parameter μare considered. Our analysis also yields asymptotical behavior of the intercepts λ^(2)(K) and λ^(3)(K). The results for λ^(2)(K) are compared with experimental data, and with earlier known results drawn using other deformed Bose gas models.

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↗

arXiv2010

Polynomially deformed oscillators as k-bonacci oscillators

A family of multi-parameter, polynomially deformed oscillators (PDOs) given by polynomial structure function ϕ(n) is studied from the viewpoint of being (or not) in the class of Fibonacci oscillators. These obey the Fibonacci relation/property (FR/FP) meaning that the n-th level energy E_n is given linearly, with real coefficients, by the two preceding ones E_{n-1}, E_{n-2}. We first prove that the PDOs do not fall in the Fibonacci class. Then, three different paths of generalizing the usual FP are developed for these oscillators: we prove that the PDOs satisfy respective k-term generalized Fibonacci (or "k-bonacci") relations; for these same oscillators we examine two other generalizations of the FR, the inhomogeneous FR and the "quasi-Fibonacci" relation. Extended families of deformed oscillators are studied too: the (q;μ)-oscillator with ϕ(n) quadratic in the basic q-number [n]_q is shown to be Tribonacci one, while the (p,q;μ)-oscillators with ϕ(n) quadratic (cubic) in the p,q-number [n]_{p,q} are proven to obey the Pentanacci (Nine-bonacci) relations. Oscillators with general ϕ(n), polynomial in [n]_{q} or [n]_{p,q}, are also studied.

math-ph↗

arXiv2010

On Chebyshev polynomials and torus knots

In this work we demonstrate that the q-numbers and their two-parameter generalization, the q,p-numbers, can be used to obtain some polynomial invariants for torus knots and links. First, we show that the q-numbers, which are closely connected with the Chebyshev polynomials, can also be related with the Alexander polynomials for the class T(s,2) of torus knots, s being an odd integer, and used for finding the corresponding skein relation. Then, we develop this procedure in order to obtain, with the help of q,p-numbers, the generalized two-variable Alexander polynomials, and prove their direct connection with the HOMFLY polynomials and the skein relation of the latter.

math-ph↗

arXiv2008

Occurrence of pairwise energy level degeneracies in q,p-oscillator model

It is demonstrated that a two-parameter deformed oscillator with the deformation parameters q,p such that 0 < q,p \le 1 exhibits the property of "accidental" two-fold (pairwise) energy level degeneracy of the classes E_m=E_{m+1} and E_0=E_{m}. The most general case of degeneracy of q,p-oscillators of the form E_{m+k}=E_m (with k\ge 1 for m\ge 1 or k\ge 2 for m=0) is briefly discussed.

quant-ph↗

arXiv2007

A q-Oscillator with 'Accidental' Degeneracy of Energy Levels

We study main features of the exotic case of q-deformed oscillators (so-called Tamm-Dancoff cutoff oscillator) and find some special properties: (i) degeneracy of the energy levels E_{n_1} = E_{n_1+1}, n_1\ge 1, at the {\em real value} q=\sqrt{\frac{n_1}{n_1+2}} of deformation parameter, as well as the occurrence of other degeneracies E_{n_1} = E_{n_1+k}, for k \ge 2, at the corresponding values of q which depend on both n_1 and k; (ii) the position and momentum operators X and P {\em commute on the state} |m> if q is fixed as q=\frac{m}{m+1}, that implies unusual uncertainty relation; (iii) two commuting copies of the creation, annihilation, and number operators of this q-oscillator generate the corresponding q-deformation of the {\em non-simple} Lie algebra su(2)\oplus u(1) whose nontrivial q-deformed commutation relation is: [ J_+, J_- ] = 2 J_0 q^{2J_3-1} where J_0\equiv \frac12 (N_1-N_2) and J_3\equiv \frac12 (N_1+N_2).

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↗

arXiv2004

Multi-particle correlations in qp-Bose gas model

The approach based on multimode system of q-deformed oscillators and the related picture of ideal gas of q-bosons enables to effectively describe the observed non-Bose type behaviour, in experiments on heavy-ion collisions, of the intercept (or the "strength") $λ$ of the two-particle correlation function of identical pions or kaons. In this paper we extend main results of that approach in the two aspects: first, we derive in explicit form the intercepts of n-particle correlation functions in the case of q-Bose gas model and, second, provide their explicit two-parameter (or qp-) generalization.

hep-ph↗

arXiv2004

Quantum algebras, particle phenomenology, and (quasi)supersymmetry

Quantum algebras U_q(su_n) used as the algebras of flavour symmetry (usually described by SU(n)) to study static properties of hadrons lead to intriguing results. In this contribution we focus on the peculiar properties manifested by different q-deformed structures (e.g., the braided line, the quantum algebras U_q(su_2) and U_q(su_n), n >= 3) in the special limit of q = -1. Similarities (complete or partial) with supersymmetry that emerge in this special limit are discussed.

hep-ph↗

arXiv2004

Applying the q-algebras U'_q(so_n) to quantum gravity: towards q-deformed analog of SO(n) spin networks

Nonstandard q-deformed algebras U'_q(so_n), proposed a decade ago for the needs of representation theory, essentially differ from the standard Drinfeld-Jimbo quantum deformation of the algebras U(so_n) and possess with regard to the latter a number of important advantages. We discuss possible application of the q-algebras U'_q(so_n), within two different contexts of quantum/q-deformed gravity: one concerns q-deforming of D-dimensional (D >= 3) euclidean gravity, the other applies to 2+1 anti-De Sitter quantum gravity (with space surface of genus g) in the approach of Nelson and Regge.

gr-qc↗

arXiv2004

Quantum groups and Cabibbo mixing

Treating the issue of hadron masses and mass relations by the use of quantum groups U_q(su_n) taken as hadron flavor symmetries suggests, at least in the case of baryons, a direct connection of the deformation parameter q with the Cabibbo angle. We discuss possible manifestations of the Cabibbo mixing implied by such connection, including unusual ones.

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↗

arXiv2002

Quantum algebras in phenomenological description of particle properties

Quantum and q-deformed algebras find their application not only in mathematical physics and field theoretical context, but also in phenomenology of particle properties. We describe (i) the use of quantum algebras U_q(su_n) corresponding to Lie algebras of the groups SU(n), taken for flavor symmetries of hadrons, in deriving new high-accuracy hadron mass sum rules, and (ii) the use of (multimode) q-oscillator algebras along with q-Bose gas picture in modelling the properties of the intercept λof two-pion (two-kaon) correlations in heavy-ion collisions, as λshows sizable observed deviation from the expected Bose-Einstein type behavior. The deformation parameter q is in case (i) argued and in case (ii) conjectured to be connected with the Cabibbo angle θ_C.

hep-ph↗

arXiv2002

q-Deformed Orthogonal and Pseudo-Orthogonal Algebras and Their Representations

Deformed orthogonal and pseudo-orthogonal Lie algebras are constructed which differ from deformations of Lie algebras in terms of Cartan subalgebra and root vectors and which make it possible to construct representations by operators acting according to Gel'fand--Tsetlin-type formulas. Unitary representations of the q-deformed algebras U_q(so_{n,1}) are found.

math.QA↗

arXiv2001

Quantum Groups as Flavor Symmetries: Account of Nonpolynomial SU(3)-Breaking Effects in Baryon Masses

The use, for flavor symmetries, of the quantum (or q-) analogs of unitary groups SU(n_f) yields new, very accurate, baryon mass sum rules. We show, in the 3-flavor case, that such approach accounts for nonpolynomial SU(3)-breaking effects in the octet and decuplet baryon masses. A version of this approach with manifestly q-covariant mass operator is given. The obtained new version of the q-deformed mass relation is simpler than those derived before, but, for its empirical validity, the parameter q is to be fixed by fitting. As shown, the well-known Gell-Mann--Okubo octet mass sum rule results, besides usual SU(3), also from an exotic "symmetry" encoded in the singular case q=-1 of the q-algebra U_q(su_3).

hep-ph↗

arXiv2001

Transverse Momentum Dependence of Intercept Parameter λof Two-Pion (-Kaon) Correlation Functions in q-Bose Gas Model

Within recently proposed approach aimed to effectively describe the observed non-Bose type behavior of the intercept λof two-particle correlation function C(p,K) of identical pions or kaons detected in heavy-ion collisions, the q-deformed oscillators and q-Bose gas picture are employed. For the intercept λ, connected with deformation parameter q, the model predicts a fully specified dependence of λon pair mean momentum {\bf K}. The intercepts λ_πand λ_K for pions and kaons, differing noticeably at small {\bf K}, should merge at {\bf K} large enough, i.e., in the range |{\bf K}| \ge 800 MeV/c, where the effect of resonance decays is negligible. In this paper we confront, fixing q appropriately, the predicted dependence λ_π=λ_π({\bf K}) with recent results from STAR/RHIC for π^-π^- and π^+π^+ pairs, and find nice agreement. Using the same q, we also predict behavior of λfor kaons.

hep-ph↗

arXiv2001

Coset-Space String Compactification Leading To 14 Subcritical Dimensions

Using sigma-model approach, we study a class of coset spaces with torsion which compactify the D=26 closed bose-string theory. Requiring also that massless chiral fermions arise from the geometry/topology of coset space, we are left with the unique possibility: it implies D=14 subcritical dimensions and the isometry group G_2 X G_2.

hep-th↗

arXiv2000

Can the Cabibbo mixing originate from noncommutative extra dimensions?

Treating hadronic flavor symmetries with quantum algebras U_q(su_n) leads to interesting consequences such as: new mass sum rules for hadrons 1^-, (1/2)^+, (3/2)^+ of improved accuracy; possibility to label different flavors topologically - by torus winding number; properly fixed deformation parameter q in case of baryons is linked in a simplest way to the Cabibbo angle θ_C, that suggests for θ_C the exact value π/{14}. In this connection, we discuss the possibility that this angle and the Cabibbo mixing as a whole take its origin in noncommutativity of some additional, with regard to 3+1, space-time dimensions.

hep-ph↗