arXiv subjects

A. M. Gavrilik

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

At least 19 recordsLinked to original sources

arXiv2026

The $q$-extension of iterated integrals and nested sums in quantum field theory

Analytic calculations of zero- and single-scale quantities in perturbative quantum field theory result into special numbers and functions, the first of which have been revealed during the last decades. These are generalizations of the polylogarithm in form of Kummer-Poincaré iterative integrals over special alphabets and extensions thereof.With growing order in the coupling constant, the polylogarithms, Nielsen integrals, the iterated integrals over linear denominator terms, cyclotomic letters, letters induced by quadratic forms, square-root valued letters, and more general functions contribute. For the nested sums we consider nested harmonic sums, generalized harmonic sums, nested sums implied by quadratic forms, cyclotomic harmonic sums, and nested sums containing central binomials. We construct the $q$-extensions of these special functions and of the nested sums, which are associated to them by the series expansion at $x=0$, and their Mellin transform in the $q$-free case. These functions are expected to play a role in perturbative calculations in the case of $q$-deformed commutation relations. For the simpler function spaces closed form solutions are presented. For more involved alphabets we present the algorithmic steps leading to the $q$-extension for the individual cases. We also derive the determining differential and difference equations of these higher transcendental functions. The $q$-extended special functions are quite different form the corresponding $μ$-extended functions.

math-ph↗

arXiv2026

The $μ$-extension of iterated integrals and nested sums

The analytic integration of single-scale Feynman integrals emerging in perturbative calculations in quantum field theories can be performed within special classes of functions, which appear as consecutive generalizations of the polylogarithm in form of Kummer-Poincaré iterative integrals over special alphabets and extensions thereof. These are the polylogarithms, Nielsen integrals, the iterated integrals over linear denominator terms, cyclotomic letters, letters induced by quadratic forms, and square-root valued letters. These integrals are solutions of first-order factorizing differential equations. They are related to specific nested sums via the Mellin transform and their expansions around $x=0$. We construct the $μ$-extensions of these iterated integrals and the associated nested sums. We present closed form solutions or provide algorithms in the case of more involved cases to derive the respective $μ$-extensions and study the algebras of the $μ$-extended function spaces. Except for the case of square-root valued alphabets, the $μ$-extension maps into the same function space polynomially in $μ$. This is also the case for the associated nested sums. For square-root valued alphabets or sums containing central binomials, the $μ$-extension leads to higher transcendental functions. In all other cases the $μ$-extension preserves the Hopf algebra structure implied by the (quasi)shuffle product, by supplementing $μ$ to the ground field.

hep-th↗

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↗

arXiv2025

Scaling behavior and phases of nonlinear sigma model on real Stiefel manifolds near two dimensions

For a quasi-two-dimensional nonlinear sigma model on the real Stiefel manifolds with a generalized (anisotropic) metric, the equations of a two-charge renormalization group (RG) for the homothety and anisotropy of the metric as effective couplings are obtained in a one-loop approximation. Normal coordinates and the curvature tensor are exploited for the renormalization of the metric. The RG trajectories are investigated and the presence of a fixed point common to four critical lines or four phases (tetracritical point) in the general case, or its absence in the case of an Abelian structure group, is established. For the tetracritical point, the critical exponents are evaluated and compared with those known earlier for a simpler particular case.

cond-mat.stat-mech↗

arXiv2023

Axionlike Dark Matter Model Involving Two-Phase Structure and Two-Particle Composites (Dimers)

Within the self-gravitating Bose-Einstein condensate (BEC) model of dark matter (DM), we argue that the axionlike self-interaction of ultralight bosons ensures the existence of both rarefied and dense phases in the DM halo core of (dwarf) galaxies. In fact, this stems from two independent solutions of the Gross-Pitaevskii equation corresponding to the same model parameters. For a small number of particles, this structure disappears along with the gravitational interaction, and the Gross-Pitaevskii equation reduces to the stationary sine-Gordon equation, the one-dimensional antikink solution of which mimics a single-phase DM radial distribution in the halo core. Quantum mechanically, this solution corresponds to a zero-energy bound state of two particles in a closed scattering channel formed by the domain-wall potential with a finite asymptotics. To produce a two-particle composite with low positive energy and a finite lifetime, we appeal to the resonant transition of one asymptotically free particle of a pair from an open channel (with a model scattering potential) to the closed channel. Using the Feshbach resonance concept, the problem of two-channel quantum mechanics is solved in the presence of a small external influence which couples the two channels, and an analytical solution is obtained in the first approximation. Analyzing the dependence of scattering data on interaction parameters, we reveal a long-lived two-particle composite (dimer) possessing a lifetime of millions of years. This result is rather surprising and supposes important implications of dimers' being involved in forming large DM structures. It is shown that the dimers' appearance is related with the regime of infinite scattering length due to resonance. The revealed dependence of the DM scattering length $a$ on the parameters of interactions can theoretically justify variation of $a$ in the DM dominated galaxies.

astro-ph.GA↗

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↗

arXiv2022

Formation of Dimers in Axion-Like Dark Matter Using the Feshbach Resonance

Within the model of self-gravitating Bose--Einstein condensate (BEC) dark matter (DM) it is argued that the axion-like self-interaction of ultralight bosons provides the existence of rarefied and dense phases, which are predicted earlier on the base of the models with polynomial-like self-interactions. Associating the very short scattering length in BEC DM with the predominant participating composites of few DM particles, we attempt to form a dimer of two particles at a quantum mechanical level, using a smooth $μ$-deformation of the axion cosine-like potential and replacing the field-dependent argument with the distance between particles. Part of the obtained results concerns potential two-particle scattering with $μ$-deformed interaction, and they allow us to focus on a special option with unique values of the deformation parameter $μ=1$ and the coupling constant. In this case of the potential with an infinite scattering length, we get a rather simple solution for the dimer in the ground state. We involve two-channel scattering and Feshbach resonance to describe the formation of a dimer in space. Specifying the parameters of interactions, we reveal a long-lived resonance that occurs when a pair of particles jumps between the open and closed scattering channels with close energy values. This indicates the possibility of participation of such dimers in forming BEC DM halo of galaxies.

astro-ph.GA↗

arXiv2022

Bose-Einstein Condensate Dark Matter That Involves Composites

By improving the Bose-Einstein condensate model of dark matter through the repulsive three-particle interaction to better reproduce observables such as rotation curves, both different thermodynamic phases and few-particle correlations are revealed. Using the numerically found solutions of the Gross-Pitaevskii equation for averaging the products of local densities and for calculating thermodynamic functions at zero temperature, it is shown that the few-particle correlations imply a first-order phase transition and are reduced to the product of single-particle averages with a simultaneous increase in pressure, density, and quantum fluctuations. Under given conditions, dark matter exhibits rather the properties of an ideal gas with an effective temperature determined by quantum fluctuations. Characteristics of oscillations between bound and unbound states of three particles are estimated within a simple random walk approach to qualitatively models the instability of particle complexes. On the other hand, the density-dependent conditions for the formation of composites are analyzed using chemical kinetics without specifying the bonds formed. The obtain results can be extended to the models of multicomponent dark matter consisting of composites formed by particles with a large scattering length.

astro-ph.GA↗

arXiv2021

Phases of the Bose-Einstein condensate dark matter model with both two- and three-particle interactions

In this paper we further elaborate on the Bose-Einstein condensate (BEC) dark matter model extended in our preceding work [Phys. Rev. D 102, 083510 (2020)] by the inclusion of 6th order (or three-particle) repulsive self-interaction term. Herein, our goal is to complete the picture through adding to the model the 4th order repulsive self-interaction. The results of our analysis confirm the following: while in the preceding work the two-phase structure and the possibility of first-order phase transition was established, here we demonstrate that with the two self-interactions involved, the nontrivial phase structure of the enriched model remains intact. For this to hold, we study the conditions which the parameters of the model, including the interaction parameters, should satisfy. As a by-product and in order to provide some illustration, we obtain the rotation curves and the (bipartite) entanglement entropy for the case of particular dwarf galaxy.

astro-ph.GA↗

arXiv2020

Bose-Einstein condensate dark matter model with three-particle interaction and two-phase structure

We explore the consequences of including the repulsive three-particle interaction in the model of Bose-Einstein condensate dark matter model or fuzzy dark matter. Such a model based on properly modified Gross-Pitaevskii equation is intended to describe the distribution of dark matter particles in the highly dense regions, which correspond to the galaxy core and/or to the overlap of colliding galaxies. Specifically, we deal with the $ϕ^6$-model in terms of the macroscopic wave function of the condensate, where a locality of interaction is guaranteed by a large correlation length assumed to hold. After calculation of main thermodynamical characteristics, we find strong evidence of the existence of two distinct phases of dark matter, within its core, separated by the instability region lying between two differing special values of the pressure acting in the model. Some implications stemming from the existence of two phases and the related first-order phase transition are discussed.

astro-ph.GA↗

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↗

arXiv2019

Photon Gas at the Planck Scale within the Doubly Special Relativity

Within the approach to doubly special relativity (DSR) suggested by Magueijo and Smolin, a new algebraically justified rule of so-called $κ$-addition for the energies of identical particles is proposed. This rule permits to introduce the nonlinear $κ$-dependent Hamiltonian for one-mode multi-photon (sub)system. On its base, with different modes treated as independent, the thermodynamics of black-body radiation is explored within DSR, and main thermodynamic quantities are obtained. In their derivation, we use both the analytical tools within mean field approximation (MFA) and numerical evaluations based on exact formulas. The entropy of one-mode subsystem turns out to be finite (bounded). Another unusual result is the existence of threshold temperature above which radiation is present. Specific features of the obtained results are explained and illustrated with a number of plots. Comparison with some works of relevance is given.

hep-th↗

arXiv2019

Statistics effects in extremal black holes ensemble

We consider the grand canonical ensemble of the static and extremal black holes, when the equivalence of the electric charge and mass of individual black hole is postulated. Assuming uniform distribution of black holes in space, we are finding the effective mass of test particle and mean time dilation at the admissible points of space, taking into account the gravitational action of surrounding black holes. Having specified the statistics that governs extremal black holes, we study its effect on those quantities. Here, the role of statistics is to assign a statistical weight to the configurations of certain fixed number of black holes. We borrow these weights from Bose-Einstein, Fermi-Dirac, classical and infinite statistics. Using mean field approximation, the aforementioned characteristics are calculated and visualized, what permits us to draw the conclusions on visible effect of each statistics.

gr-qc↗

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↗