arXiv subjects

A. V. Nazarenko

Publications and source records attributed to A. V. Nazarenko.

At least 19 recordsLinked to original sources

arXiv2026

Axionlike dark-matter winds driven by galactic baryon redistribution

We examine solutions of the hydrodynamic equations for dark matter (DM) modeled as a Bose-Einstein condensate (BEC) with axionlike interaction, forming a spherically symmetric halo in dwarf galaxies. Small perturbations and decoherence of the BEC DM arise from changes in the gravitational background induced by subgalactic baryonic processes. Focusing on the events in the central region of a galaxy, overlapping with the stable DM core, we consider three scenarios: (i) expansion of a gaseous shell mimicking stellar explosions, (ii) collapse of a shell modeling star formation, and (iii) contraction of a stellar cluster toward the galactic center, driven by dynamical friction within a gaseous shell. Numerical parameters are extracted from observational data for NGC 2366. Our results show central DM density increases of 0.01 percent and DM wind velocities of up to several meters per second. A greater increase in density is observed at lower wind speeds and vice versa. These results raise the question of whether minor DM variations significantly affect star formation. In analyzing the fate of the cumulative impact of baryonic processes, we turn to the quantum excitation model with a discrete spectrum in finite volume. In the inhomogeneous DM halo, including unstable phase, metastable excitations associated with false vacuum states decay over 32 million years. This induces the decay of the system's evolutionary operator. Meanwhile, the Beliaev damping, originating from the decay of stable quasiparticles, emerges in the next order of perturbation.

astro-ph.GA↗

arXiv2025

Macroscopic states in Bose-Einstein condensate dark matter model with axionlike interaction

The phase diagrams of ultralight dark matter (DM), modeled as a self-gravitating Bose-Einstein condensate with axionlike interaction, are studied. We classify stable, metastable, and unstable DM states over a wide range of condensate wave function amplitudes. It is shown that the axionlike interaction causes instability and an imaginary speed of sound at low amplitudes, whereas, in a specific high-amplitude band, DM attains a stable state capable of forming a dense solitonic core and suppressing quantum fluctuations in the surrounding galactic DM halo. These findings are corroborated by evaluating thermodynamic functions for DM in the dwarf galaxy NGC 2366 and its hypothetical analogs with different core-to-halo mass ratios. Distinct DM phase compositions respond differently to fluctuation-induced partial pressure, resulting in a first-order phase transition in a certain range of an interaction parameter. While the DM properties in NGC 2366 lie within the supercritical regime, the phase transition nonetheless provides a thermodynamic marker separating stable from unstable DM configurations. Once a dense core forms - reaching a threshold of about 12% of the total mass - the enhanced gravitation stabilizes the DM halo against fluctuations, while the internal pressure ensures core stability. In particular, we find that NGC 2366's dense DM comprises roughly 19% of the DM mass while occupying only 4.7% of its total volume.

astro-ph.GA↗

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↗

arXiv2024

Structures associated with the Borromean rings complement in the Poincaré ball

Guided by physical needs, we deal with the rotationally isotropic Poincaré ball, when considering the complement of Borromean rings embedded in it. We consistently describe the geometry of the complement and realize the fundamental group as isometry subgroup in three dimensions. Applying this realization, we reveal normal stochastization and multifractal behavior within the examined model of directed random walks on the rooted Cayley tree, whose six-branch graphs are associated with dendritic polymers. According to Penner, we construct the Teichmüller space of the decorated ideal octahedral surface related to the quotient space of the fundamental group action. Using the conformality of decoration, we define six moduli and the mapping class group generated by cyclic permutations of the ideal vertices. Intending to quantize the geometric area, we state the connection between the induced geometry and the sine-Gordon model. Due to such a correspondence we obtain the differential two-form in the cotangent bundle.

math-ph↗

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↗

arXiv2020

Partition Function of the Bose-Einstein Condensed Dark Matter and the Modified Gross-Pitaevskii Equation

Intending to describe the dark matter of dwarf galaxies, we concentrate on one model of the slowly rotating and gravitating Bose-Einstein condensate. For a deeper understanding of its properties, we calculate the partition function and compare the characteristics derived from it with the results based on the solution of Gross-Pitaevskii equation. In our approach, which uses the Green's functions of spatial evolution operators, we formulate in a unified way the boundary conditions, important for applying the Thomas-Fermi approximation. Taking this into account, we revise some of the results obtained earlier. We also derive the spatial particle distribution, similar to the model with rotation, by using the deformation of commutation relations for a macroscopic wave function and modifying the Gross-Pitaevskii equation. It is shown that such an approach leads to the entropy inhomogeneity and makes the distribution dependent on temperature.

astro-ph.GA↗

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↗

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↗

arXiv2017

Asymmetric Random Walk in a One-Dimensional Multi-Zone Environment

We consider a random walk model in a one-dimensional environment, formed by several zones of finite width with the fixed transition probabilities. It is also assumed that the transitions to the left and right neighboring points have unequal probabilities. In continuous limit, we derive analytically the probability distribution function, which is mainly determined by a walker diffusion and drift and accounts perturbatively for interface effects between zones. It is used for computing the probability to find a walker in a given space-time point and the time dependence of the mean squared displacement of a walker, which reveals the transient anomalous diffusion. To justify our approach, the probability function is compared with the results of numerical simulations for a three-zone environment.

cond-mat.stat-mech↗

arXiv2017

One-Dimensional Random Walk in Multi-Zone Environment

We study a symmetric random walk (RW) in one spatial dimension in environment, formed by several zones of finite width, where the probability of transition between two neighboring points and corresponding diffusion coefficient are considered to be differently fixed. We derive analytically the probability to find a walker at the given position and time. The probability distribution function is found and has no Gaussian form because of properties of adsorption in the bulk of zones and partial reflection at the separation points. Time dependence of the mean squared displacement of a walker is studied as well and revealed the transient anomalous behavior as compared with ordinary RW.

cond-mat.stat-mech↗

arXiv2016

Relativistic Kinematics of Two-Parametric Riemann Surface in Genus Two

It is considered a model of compact Riemann surface in genus two, represented geometrically by two-parametric hyperbolic octagon with an order four automorphism and described algebraically by the corresponding Fuchsian group. Introducing the Fenchel--Nielsen variables, we compute the Weil--Petersson (WP) symplectic two-form for parameter space and analyze the closed isoperimetric orbits of octagons. WP-Area in parameter space and the canonical action--angle variables for the orbits are found. Exploiting the ideas from the loop quantum gravity, we generate relativistic kinematics by the Lorentz boost and quantize WP-area. We treat the evolution in terms of global variables within the "big bounce" concept.

math-ph↗