arXiv subjects

D. V. Anchishkin

Publications and source records attributed to D. V. Anchishkin.

18 recordsLinked to original sources

arXiv2020

Thermodynamic properties of interacting bosons with zero chemical potential

Thermodynamics properties of an interacting system of bosons are considered at finite temperatures and zero chemical potential within the Skyrme-like mean-field model. An interplay between attractive and repulsive interactions is investigated. As a particular example an equilibrium system of pions is discussed. Several modifications of thermodynamic properties in the considered system are found with increasing a strength of attractive forces. Different types of the first order phase transition are classified. Some of these transitions exist also in the Boltzmann approximation. However, effects of the Bose statistics introduce the notable additional changes in the thermodynamic quantities due to a possibility of the Bose-Einstein condensation.

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arXiv2019

Condensation of interacting scalar bosons at finite temperatures

Thermodynamical properties of an interacting system of scalar bosons at finite temperatures are studied within the framework of a field-theoretical model containing the attractive and repulsive self-interaction terms. Self-consistency relations between the effective mass and thermodynamic functions are derived in the mean-field approximation. We show that for a sufficiently strong attractive interaction a first-order phase transition develops in the system via the formation of a scalar condensate. An interesting prediction of this model is that the condensed phase appears within a finite temperature interval and is characterized by a constant scalar density of Bose particles.

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arXiv2017

Quantum van der Waals and Walecka models of nuclear matter

A comparable study of the quantum van der Waals and Walecka models of nuclear matter is presented. Each model contains two parameters which characterize the repulsive and attractive interactions between nucleons. These parameters are fixed in order to reproduce the known properties of the nuclear ground state. Both models predict a first-order liquid-gas phase transition and a very similar behavior in the vicinity of the critical point. Critical exponents of the quantum van der Waals model are studied both analytically and numerically. There are important differences in the behavior of the thermodynamical functions of the considered models at large values of the nucleon number density. At the same time both models fall into the universality class of mean-field theory.

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arXiv2016

Critical fluctuations in models with van der Waals interactions

Particle number fluctuations are considered within the van der Waals (VDW) equation, which contains both attractive (mean-field) and repulsive (eigenvolume) interactions. The VDW equation is used to calculate the scaled variance of particle number fluctuations in generic Boltzmann VDW system and in nuclear matter. The strongly intensive measures $Δ[E^*,N]$ and $Σ[E^*,N]$ of the particle number and excitation energy fluctuations are also considered, and, similarly, show singular behavior near the critical point. The $Δ[E^*,N]$ measure is shown to attain both positive and negative values in the vicinity of critical point. Based on universality argument, similar behavior is expected to occur in the vicinity of the QCD critical point.

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arXiv2016

Limiting temperature of pion gas with the van der Waals equation of state

The grand canonical ensemble formulation of the van der Waals equation of state that includes the effects of Bose statistics is applied to an equilibrium system of interacting pions. If the attractive interaction between pions is large enough, a limiting temperature $T_0$ emerges, i.e., no thermodynamical equilibrium is possible at $T>T_0$. The system pressure $p$, particle number density $n$, and energy density $\varepsilon$ remain finite at $T=T_0$, whereas for $T$ near $T_0$ both the specific heat $C=d\varepsilon/dT$ and the scaled variance of particle number fluctuations $ω[N]$ are proportional to $(T_0-T)^{-1/2}$ and, thus, go to infinity at $T\rightarrow T_0$. The limiting temperature corresponds also to the softest point of the equation of state, i.e., the speed of sound squared $c_s^2=dp/d\varepsilon$ goes to zero as $(T_0-T)^{1/2}$. Very similar thermodynamical behavior takes place in the Hagedorn model for the special choice of a power, namely $m^{-4}$, in the pre-exponential factor of the mass spectrum $ρ(m)$.

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arXiv2015

Non-Gaussian particle number fluctuations in vicinity of the critical point for van der Waals equation of state

The non-Gaussian measures of the particle number fluctuations -- skewness $Sσ$ and kurtosis $κσ^2$ -- are calculated in a vicinity of the critical point. This point corresponds to the end point of the first-order liquid-gas phase transition. The gaseous phase is characterized by the positive values of skewness while the liquid phase has negative skew. The kurtosis appears to be significantly negative at the critical density and supercritical temperatures. The skewness and kurtosis diverge at the critical point. The classical van der Waals equation of state in the grand canonical ensemble formulation is used in our studies. Neglecting effects of the quantum statistics we succeed to obtain the analytical expressions for the rich structures of the skewness and kurtosis in a wide region around the critical point. These results have universal form, i.e., they do not depend on particular values of the van der Waals parameters $a$ and $b$. The strongly intensive measures of particle number and energy fluctuations are also considered and show singular behavior in the vicinity of the critical point.

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arXiv2015

Scaled variance, skewness, and kurtosis near the critical point of nuclear matter

The van der Waals (VDW) equation of state predicts the existence of a first-order liquid-gas phase transition and contains a critical point. The VDW equation with Fermi statistics is applied to a description of the nuclear matter. The nucleon number fluctuations near the critical point of nuclear matter are studied. The scaled variance, skewness, and kurtosis diverge at the critical point. It is found that the crossover region of the phase diagram is characterized by the large values of the scaled variance, the almost zero skewness, and the significantly negative kurtosis. The rich structures of the skewness and kurtosis are observed in the phase diagram in the wide region around the critical point, namely, they both may attain large positive or negative values.

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arXiv2015

Van der Waals Equation of State with Fermi Statistics for Nuclear Matter

The van der Waals (VDW) equation of state is a simple and popular model to describe the pressure function in equilibrium systems of particles with both repulsive and attractive interactions. This equation predicts an existence of a first-order liquid-gas phase transition and contains a critical point. Two steps to extend the VDW equation and make it appropriate for new physical applications are carried out in this paper: 1) the grand canonical ensemble formulation; 2) an inclusion of the quantum statistics. The VDW equation with Fermi statistics is then applied to a description of the system of interacting nucleons. The VDW parameters $a$ and $b$ are fixed to reproduce the properties of nuclear matter at saturation density $n_0=0.16$ fm$^{-3}$ and zero temperature. The model predicts a location of the critical point for the symmetric nuclear matter at temperature $T_c\cong 19.7$ MeV and nucleon number density $n_c \cong 0.07$ fm$^{-3}$.

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arXiv2015

Particle Number Fluctuations for van der Waals Equation of State

The van der Waals (VDW) equation of state describes a thermal equilibrium in system of particles, where both repulsive and attractive interactions between them are included. This equation predicts an existence of the 1st order liquid-gas phase transition and the critical point. The standard form of the VDW equation is given by the pressure function in the canonical ensemble (CE) with a fixed number of particles. In the present paper the VDW equation is transformed to the grand canonical ensemble (GCE). We argue that this procedure can be useful for new physical applications. Particularly, the fluctuations of number of particles, which are absent in the CE, can be studied in the GCE. For the VDW equation of state in the GCE the particle number fluctuations are calculated for the whole phase diagram, both outside and inside the liquid-gas mixed phase region. It is shown that the scaled variance of these fluctuations remains finite within the mixed phase and goes to infinity at the critical point. The GCE formulation of the VDW equation of state can be also an important step for its application to a statistical description of hadronic systems, where numbers of different particle species are usually not conserved.

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arXiv2015

Mean transverse mass of hadrons in proton-proton reactions

An energy dependence of the mean transverse mass $\langle m_T\rangle$ at mid-rapidity in proton-proton ($p+p$) reactions is studied within the ultra-relativistic quantum molecular dynamics (UrQMD). The UrQMD model predicts a nonmonotonous dependence of $\langle m_T\rangle$ on collision energy for several hadron species: for $π^+$, $p$, $K^+$, and $Λ$ the mean transverse mass has a maximum at the center of mass energy region $5\le \sqrt{s}\le 8$ GeV. These results are a consequence of an interplay of two contributions: 1) excitations and decays of the baryonic resonances $N^*$ and $Δ$; 2) excitations and decays of the baryonic strings. The UrQMD results do not show any nonmonotonous dependence of $\langle m_T\rangle$ on $\sqrt{s}$ for $π^-$, $K^{-}$, and antiprotons. Whether a nonmonotonous dependence of $\langle m_T\rangle$ at mid-rapidity on the collision energy for $π^+$, $p$, $K^+$, and $Λ$ is relevant for real $p+p$ interactions will be soon checked experimentally by the NA61/SHINE Collaboration.

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arXiv2015

Hadron Resonance Gas Equation of State from Lattice QCD

The Monte Carlo results in lattice QCD for the pressure and energy density at small temperature $T < 155$ MeV and zero baryonic chemical potential are analyzed within the hadron resonance gas model. Two extensions of the ideal hadron resonance gas are considered: the excluded volume model which describes a repulsion of hadrons at short distances and Hagedorn model with the exponential mass spectrum. Considering both of these models one by one we do not find the conclusive evidences in favor of any of them. The controversial results appear because of rather different sensitivities of the pressure and energy density to both excluded volume and Hagedorn mass spectrum effects. On the other hand, we have found a clear evidence for a simultaneous presence of both of them. They lead to rather essential contributions: suppression effects for thermodynamical functions of the hadron resonance gas due to the excluded volume effects and enhancement due to the Hagedorn mass spectrum.

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arXiv2014

System-size and energy dependence of particle momentum spectra: The UrQMD analysis of p+p and Pb+Pb collisions

The UrQMD transport model is used to study a system-size and energy dependence of the pion production in high energy collisions. New data of the NA61/SHINE Collaboration on spectra of negatively charged pions in proton-proton interactions at SPS energies are considered. These results are compared with the corresponding data of the NA49 Collaboration in central Pb+Pb collisions at the same collision energies per nucleon. Mean pion multiplicity per participant nucleon, inverse slope parameter of the transverse momentum spectra, and width of rapidity distribution are investigated. A role of isospin effects is discussed. We find that the UrQMD model predicts a non-monotonous behavior of mean transverse mass with collision energy for positively charged pions at the mid-rapidity in inelastic proton-proton interactions. This will be checked soon experimentally by NA61/SHINE Collaboration.

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arXiv2006

Liquid-like phases of π^+π^- matter

To give a common theoretical description of liquid phases of the charged pion matter in a wide temperature interval, the relativistic quantum $ϕ^6$ type model is considered. The liquid states of pion condensate and hot pion matter are investigated.

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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↗

arXiv2000

q-Boson approach to multiparticle correlations

An approach is proposed enabling to effectively describe, for relativistic heavy-ion collisions, the observed deviation from unity of the intercept λ(measured value corresponding to zero relative momentum {\bf p} of two registered identical pions or kaons) of the two-particle correlation function C(p,K). The approach uses q-deformed oscillators and the related picture of ideal gas of q-bosons. In effect, the intercept λis connected with deformation parameter q. For a fixed value of q, the model predicts specific dependence of λon pair mean momentum {\bf K} so that, when |{\bf K}|\gsim 500 - 600 MeV/c for pions or when |{\bf K}|\gsim 700 - 800 MeV/c for kaons, the intercept λtends to a constant which is less than unity and determined by q. If q is fixed to be the same for pions and kaons, the intercepts λ_πand λ_K essentially differ at small mean momenta {\bf K}, but tend to be equal at {\bf K} large enough (|{\bf K}|\gsim 800MeV/c) where the effect of resonance decays can be neglected. We argue that it is of basic interest to check in the experiments on heavy ion collisions: (i) the exact shape of dependence λ= λ({\bf K}), and (ii) whether for |{\bf K}| \gsim 800 MeV/c the resulting λ_πand λ_K indeed coincide.

hep-ph↗

arXiv1999

Two-Particle Correlations from the q-Boson Viewpoint

We propose and develop to some extent a novel approach, which allows us to effectively describe, for relativistic heavy-ion collisions, the empirically observed deviation from unity of the intercept λ(i.e. the measured value corresponding to zero relative momentum {\bf p} of two registered identical pions or kaons) of the two-particle correlation function C(p,K). The approach is based on the use of two versions of the so-called q-deformed oscillators and the corresponding picture of ideal gases of q-bosons. By these techniques the intercept λis put into direct correspondence with the deformation parameter q. For fixed deformation strength, the model predicts dependence of the intercept λon the pion pair mean momentum {\bf K}.

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arXiv1999

The Influence of High Multiplicities at RHIC on the Gamov Factor

The corrections for two-pion correlations due to electromagnetic final-state interactions at high secondary multiplicities are investigated. The analysis is performed by solving the Schrödinger equation with a potential which is dictated by the multi-particle environment. Two different post-freeze-out scenarios are examined. First, for a uniformly spread environment of secondary particles, a screened Coulomb potential is exploited. It is shown that the presence of a static and uniform post-freeze-out medium results in a noticeable deviation from the standard Gamov factor. However, after going to a more realistic model of an expanding pion system, this conclusion changes drastically. We argue that the density of the secondary pions n_π(t,R), where R is a distance from the fireball, is bounded from above by n_π(t,R)\le const/R^2 for all times t. Then, a two-particle scalar potential which is found as a solution of the Maxwell equation for non-uniform medium replaces the screened one. Even this upper limit does not result in an essential deviation from the Gamov correction.

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arXiv1995

Coulomb Final State Interaction in Pion Interferometry for the Processes of High Multiplicity

The corrections for two pion correlations due to electromagnetic final state interactions at high secondary multiplicities are investigated. It is shown that these result in a noticeable deviation from the standard Gamov factor. This conclusion changes drastically in a model of the pion system with expansion. The critical parameter which determines the size of these effects is found to be the ratio of the relative velocity of detected pions to the velocity of the pair center-of-mass (in the fireball rest frame). In particular, when this parameter is much less than unity the pion pair escapes the initial high density region promptly and the distortion of the mutual Coulomb potential is weak.

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