My publicaions
Check out my INSPIREHEP and Google Scholar profiles for detailed publication records.
Below you can find the list of my publications.

Proton and $\Lambda$ flow and the equation of state at high density
Abstract
Results on proton and Λ flow, calculated with the UrQMD model that incorporates different realistic density dependent equations of state, are presented. It is shown that the proton and hyperon flow shows sensitivity to the equation of state and especially to the appearance of a phase transition at densities below 4n0. Even though qualitatively hyperons and protons exhibit the same beam energy dependence of the flow, the quantitative results are different. In this context it is suggested that the hyperon measurements can be used to study the density dependence of the hyperon interaction in high density QCD matter.

Jan Steinheimer, Manjunath Omana Kuttan, Anton Motornenko, Agnieszka Sorensen, Yasushi Nara, Volker Koch, Marcus Bleicher, Horst Stoecker
EPJ Web Conf. 276 (2023) 01021

Dense Nuclear Matter Equation of State from HeavyIon Collisions
Abstract
The nuclear equation of state (EOS) is at the center of numerous theoretical and experimental efforts in nuclear physics. With advances in microscopic theories for nuclear interactions, the availability of experiments probing nuclear matter under conditions not reached before, endeavors to develop sophisticated and reliable transport simulations to interpret these experiments, and the advent of multimessenger astronomy, the next decade will bring new opportunities for determining the nuclear matter EOS, elucidating its dependence on density, temperature, and isospin asymmetry. Among controlled terrestrial experiments, collisions of heavy nuclei at intermediate beam energies (from a few tens of MeV/nucleon to about 25 GeV/nucleon in the fixedtarget frame) probe the widest ranges of baryon density and temperature, enabling studies of nuclear matter from a few tenths to about 5 times the nuclear saturation density and for temperatures from a few to well above a hundred MeV, respectively. Collisions of neutronrich isotopes further bring the opportunity to probe effects due to the isospin asymmetry. However, capitalizing on the enormous scientific effort aimed at uncovering the dense nuclear matter EOS, both at RHIC and at FRIB as well as at other international facilities, depends on the continued development of stateoftheart hadronic transport simulations. This white paper highlights the role that heavyion collision experiments and hadronic transport simulations play in understanding strong interactions in dense nuclear matter, with an emphasis on how these efforts can be used together with microscopic approaches and neutron star studies to uncover the nuclear EOS.

Agnieszka Sorensen, Kshitij Agarwal, Kyle W. Brown, Zbigniew Chajecki, Paweł Danielewicz, et al.
ePrint: 2301.13253 [nuclth]

Gravitational Waves from a Core gMode in Supernovae as Probes of the HighDensity Equation of State
Abstract
Using relativistic supernova simulations of massive progenitor stars with a quarkhadron equation of state (EoS) and a purely hadronic EoS, we identify a distinctive feature in the gravitationalwave signal that originates from a buoyancydriven mode (gmode) below the protoneutron star convection zone. The mode frequency lies in the range $200\lesssim f\lesssim 800\,\text{Hz}$ and decreases with time. As the mode lives in the core of the protoneutron star, its frequency and power are highly sensitive to the EoS, in particular the sound speed around twice saturation density.

Pia Jakobus, Bernhard Müller, Alexander Heger, Shuai Zha, Jade Powell, Anton Motornenko, Jan Steinheimer, Horst Stoecker
ePrint: 2301.06515 [astroph.HE]

Phase transition amplification of proton number fluctuations in nuclear collisions from a transport model approach
Abstract
The time evolution of particle number fluctuations in nuclear collisions at intermediate energies ($E_{\rm lab} = 1.2310A$ GeV) is studied by means of the UrQMD3.5 transport model. The transport description incorporates baryonic interactions through a densitydependent potential. This allows for an implementation of a first order phase transition including a mechanically unstable region at large baryon density. The scaled variance of the baryon and proton number distributions is calculated in the central cubic spatial volume of the collisions at different times. A significant enhancement of fluctuations associated with the unstable region is observed. This enhancement persists to late times reflecting a memory effect for the fluctuations. The presence of the phase transition has a much smaller influence on the observable eventbyevent fluctuations of protons in momentum space.

Oleh Savchuk, Roman V. Poberezhnyuk, Anton Motornenko, Jan Steinheimer, Mark I. Gorenstein, Volodymyr Vovchenko
Phys.Rev.C 107 (2023) 024913
ePrint: 2211.13200 [hepph]

Enhanced dilepton emission from a phase transition in dense matter
Abstract
It is demonstrated that the presence of a phase transition in heavy ion collisions, at beam energies that probe dense QCD matter, leads to a significant enhancement of the dilepton yield per produced pion due to the extended emission time. In addition, the temperature of low mass dileptons shows a modest decrease due to the mixed phase. The emission of dileptons in the SIS18SIS100 beam energies range is studied by augmenting the UrQMD transport model with a realistic density dependent equation of state, as well as two different phase transitions. This is achieved by extending the molecular dynamics interaction part of the UrQMD model to a density dependent interaction potential with a high density minimum leading to a phase transition and metastable coexisting high density states. Together with a high precision measurement these simulations will be able to constrain the existence of a phase transition in QCD up to densities of several times nuclear saturation density.

O. Savchuk, A. Motornenko, J. Steinheimer, V. Vovchenko, M. Bleicher, M. Gorenstein, T. Galatyuk
ePrint: 2209.05267 [nuclth]

The highdensity equation of state in heavyion collisions: constraints from proton flow
Abstract
A set of different equations of state is implemented in the molecular dynamics part of a nonequilibrium transport simulation (UrQMD) of heavyion collisions. It is shown how different flow observables are affected by the density dependence of the equation of state. In particular, the effects of a phase transition at high density are explored, including an expected reduction in mean $m_T$. We also show that an increase in $v_2$ is characteristic for a strong softening of the equation of state. The phase transitions with a low coexistence density, $n_{\mathrm{CE}}<4 n_0$, show a distinct minimum in the slope of the directed flow as a function of the beam energy, which would be a clear experimental signal. By comparing our results with experimental data, we can exclude any strong phase transition at densities below $4n_0$.

Jan Steinheimer, Anton Motornenko, Agnieszka Sorensen, Yasushi Nara, Volker Koch, Marcus Bleicher
Eur.Phys.J.C 82 (2022) 911
ePrint: 2208.12091 [nuclth]

The role of the hadronquark phase transition in corecollapse supernovae
Abstract
The hadronquark phase transition in quantum chromodyanmics has been suggested as an alternative explosion mechanism for corecollapse supernovae. We study the impact of three different hadronquark equations of state (EoS) with firstorder (DD2F_SF, STOSB145) and secondorder (CMF) phase transitions on supernova dynamics by performing 97 simulations for solar and zerometallicity progenitors in the range of $14\texttt{}100\,\text{M}_\odot$. We find explosions only for two lowcompactness models ($14 \text{M}_\odot$ and $16\,\text{M}_\odot$) with the DD2F_SF EoS, both with low explosion energies of $\mathord{\sim}10^{50}\,\mathrm{erg}$. These weak explosions are characterised by a neutrino signal with several minibursts in the explosion phase due to complex reverse shock dynamics, in addition to the typical second neutrino burst for phasetransition driven explosions. The nucleosynthesis shows significant overproduction of nuclei such as $^{90}\mathrm{Zr}$ for the $14\,\text{M}_\odot$ zerometallicity model and $^{94}\mathrm{Zr}$ for the $16\,\text{M}_\odot$ solarmetallicity model, but the overproduction factors are not large enough to place constraints on the occurrence of such explosions. Several other lowcompactness models using the DD2F_SF EoS and two highcompactness models using the STOS EoS end up as failed explosions and emit a second neutrino burst. For the CMF EoS, the phase transition never leads to a second bounce and explosion. For all three EoS, inverted convection occurs deep in the core of the protocompact star due to anomalous behaviour of thermodynamic derivatives in the mixed phase, which heats the core to entropies up to $4k_\text{B}/\text{baryon}$ and may have a distinctive gravitational wave signature, also for a secondorder phase transition.

Pia Jakobus, Bernhard Mueller, Alexander Heger, Anton Motornenko, Jan Steinheimer, Horst Stoecker
Mon.Not.Roy.Astron.Soc. 516 (2022)
ePrint: 2204.10397 [astroph.HE]


Anton Motornenko, Somenath Pal, Abhijit Bhattacharyya, Jan Steinheimer, Horst Stoecker

Probing neutronstar matter in the lab: Similarities and differences between binary mergers and heavyion collisions
Abstract
As a way to find analogies and differences in the dynamics of hot and dense matter under extreme conditions, we present the first selfconsistent relativistichydrodynamic calculations of both neutronstar mergers and lowenergy heavyion collisions employing the same equation of state. By a direct comparison of the evolution of quantities such as temperature, entropy, and density, we show that neutronstar collision regimes can be probed directly at GSI beam energies. We provide concrete evidence that the physical conditions reached in binary neutronstar mergers can be studied in present and future laboratory experiments, thus bridging 18 orders of magnitude in length scale, from microscopic ion collisions to macroscopic astrophysical compact objects.

Elias R. Most, Anton Motornenko, Jan Steinheimer, Veronica Dexheimer, Matthias Hanauske, Luciano Rezzolla, Horst Stoecker
Phys.Rev.D 107 (2023) 043034
ePrint: 2201.13150 [nuclth]

A chiral meanfield equationofstate in UrQMD: effects on the heavy ion compression stage
Abstract
It is shown that the initial compression in central heavy ion collisions at beam energies of $E_\mathrm{lab}=110A$~GeV depends dominantly on the underlying equation of state and only marginally on the model used for the dynamical description. To do so, a procedure to incorporate any equation of state in the UrQMD transport model is introduced. In particular we compare the baryon density, temperature and pressure evolution as well as produced entropy in a relativistic ideal hydrodynamics approach and the UrQMD transport model, where the same equation of state is used in both approaches. Not only is the compression similar if the same equation of state is used in either dynamical model, but it also strongly depends on the actual equation of state. These results indicate that the equation of state can be studied with observables which are sensitive to the initial compression phase and maximum compression achieved in heavy ion collisions at these beam energies.

Manjunath Omana Kuttan, Anton Motornenko, Jan Steinheimer, Horst Stoecker, Yasushi Nara, Marcus Bleicher
Eur.Phys.J.C 82 (2022) 427
ePrint: 2201.01622 [nuclth]

Heavy ion collisions and neutron stars : dynamics and thermodynamics of QCD matter
Abstract
This thesis deals with the phenomenology of QCD matter, its aspects in heavy ion collisions and in neutron stars. The first half of the work focuses on the hadronic phase of QCD matter. One focus is on how the hadronic phase shows itself in heavy ion collisions and how its dynamics can be simulated. The role of hadronic interactions is considered in the context of the lattice QCD data. The second part of this thesis presents a unified approach to QCD matter, the CMF model. The CMF model incorporates many aspects of QCD phenomenology which allows for a consistent description of the hadronquark transition, making it applicable to the entire QCD phase diagram, i.e., to the cold nuclear matter and to the hot QCD matter. It is shown that a description of both the hot matter created in heavy ion collisions and the cold dense matter in neutron star interiors is possible within one single approach, the CMF model.

Anton Motornenko
PhD thesis

From cosmic matter to the laboratory
Abstract
The recent discovery of binary neutron star mergers has opened a new and exciting venue of research into hot and dense strongly interacting matter. For the first time this elusive state of matter, described by the theory of quantum chromo dynamics, can be studied in two very different environments. On the macroscopic scale in the collisions of neutron stars and on the microscopic scale in collisions of heavy ions at particle collider facilities. We will discuss the conditions that are created in these mergers and the corresponding high energy nuclear collisions. This includes the properties of QCD matter, i.e. the expected equation of state as well as expected chemical and thermodynamic properties of this exotic matter. To explore this matter in the laboratory  a new research prospect is available at the Facility for Antiproton and Ion Research, FAIR. The new facility is being constructed adjacent to the existing accelerator complex of the GSI Helmholtz Center for Heavy Ion Research at Darmstadt/Germany, expanding the research goals and technical possibilities substantially. The worldwide unique accelerator and experimental facilities of FAIR will open the way for a broad spectrum of unprecedented research supplying a variety of experiments in hadron, nuclear, atomic and plasma physics as well as biomedical and material science which will be briefly described.

Anton Motornenko, Jan Steinheimer, Horst Stoecker
ePrint: 2105.12475 [nuclth]

Ambiguities in the hadrochemical freezeout of Au+Au collisions at SIS18 energies and how to resolve them
Abstract
The thermal fit to preliminary HADES data of Au+Au collisions at $\sqrt{s_{_{NN}}}=2.4$ GeV shows two degenerate solutions at $T\approx50$ MeV and $T\approx70$ MeV. The analysis of the same particle yields in a transport simulation of the UrQMD model yields the same features, i.e. two distinct temperatures for the chemical freezeout. While both solutions yield the same number of hadrons after resonance decays, the feeddown contribution is very different for both cases. This highlights that two systems with different chemical composition can yield the same multiplicities after resonance decays. The nature of these two minima is further investigated by studying the timedependent particle yields and extracted thermodynamic properties of the UrQMD model. It is confirmed, that the evolution of the high temperature solution resembles cooling and expansion of a hot and dense fireball. The low temperature solution displays an unphysical evolution: heating and compression of matter with a decrease of entropy. These results imply that the thermal model analysis of systems produced in low energy nuclear collisions is ambiguous but can be interpreted by taking also the time evolution and resonance contributions into account.

Anton Motornenko, Jan Steinheimer, Volodymyr Vovchenko, Reinhard Stock, Horst Stoecker
Phys.Lett.B 822 (2021) 136703
ePrint: 2104.06036 [hepph]

Repulsive properties of hadrons in lattice QCD data and neutron stars
Abstract
Secondorder susceptibilities $\chi^{11}_{ij}$ of baryon, electric, and strangeness, $B$, $Q$, and $S$, charges, are calculated in the Chiral Mean Field (CMF) model and compared to available lattice QCD data. The susceptibilities are sensitive to the short range repulsive interactions between different hadron species, especially to the hardcore repulsion of hyperons. Decreasing the hyperons size, as compared to the size of the nonstrange baryons, does improve significantly the agreement of the CMF model results with the Lattice QCD data. The electric chargedependent susceptibilities are sensitive to the short range repulsive volume of mesons. The comparison with lattice QCD data suggests that strange baryons, nonstrange mesons and strange mesons have significantly smaller excluded volumes than nonstrange baryons. The CMF model with these modified hadron volumes allows for a mainly hadronic description of the QCD susceptibilities significantly above the chiral pseudocritical temperature. This improved CMF model which is based on the lattice QCD data, has been used to study the properties of both cold QCD matter and neutron star matter. The phase structure in both cases is essentially unchanged, i.e. a chiral firstorder phase transition occurs at low temperatures ($T_{\rm CP}\approx 17$ MeV), and hyperons survive deconfinement to higher densities than nonstrange hadrons. The neutron star maximal mass remains close to 2.1$M_\odot$ and the massradius diagram is only modified slightly due to the appearance of hyperons and is in agreement with astrophysical observations.

Anton Motornenko, Somenath Pal, Abhijit Bhattacharyya, Jan Steinheimer, Horst Stoecker
Phys.Rev.C 103 (2021) 054908
ePrint: 2009.10848 [hepph]

Laser wake field collider
Abstract
Recently NAanoPlasmonic, Laser Inertial Fusion Experiments (NAPLIFE) were proposed, as an improved way to achieve laser driven fusion. The improvement is the combination of two basic research discoveries: (i) The possibility of detonations on spacetime hypersurfaces with timelike normal (i.e. simultaneous detonation in a whole volume) and (ii) to increase this volume to the whole target, by regulating the laser light absorption using nanoshells or nanorods as antennas. These principles can be realized in an inline, one dimensional configuration, in the simplest way with two opposing laser beams as in particle colliders. Such, opposing laser beam experiments were also performed recently. Here we study the consequences of the Laser Wake Field Acceleration (LWFA) if we experience it in a colliding laser beam set up. These studies can be applied to laser driven fusion, but also to other rapid phase transition, combustion, or ignition studies in other materials.

István Papp, Larissa Bravina, Mária Csete, Igor N. Mishustin, Dénes Molnár, et al.
Phys.Lett.A 396 (2021) 127245
ePrint: 2009.03686 [physics.plasmph]

Identifying the nature of the QCD transition in heavyion collisions with deep learning
Abstract
In this proceeding, we review our recent work using deep convolutional neural network (CNN) to identify the nature of the QCD transition in a hybrid modeling of heavyion collisions. Within this hybrid model, a viscous hydrodynamic model is coupled with a hadronic cascade "afterburner". As a binary classification setup, we employ two different types of equations of state (EoS) of the hot medium in the hydrodynamic evolution. The resulting finalstate pion spectra in the transverse momentum and azimuthal angle plane are fed to the neural network as the input data in order to distinguish different EoS. To probe the effects of the fluctuations in the eventbyevent spectra, we explore different scenarios for the input data and make a comparison in a systematic way. We observe a clear hierarchy in the predictive power when the network is fed with the eventbyevent, cascadecoarsegrained and eventfineaveraged spectra. The carefullytrained neural network can extract highlevel features from pion spectra to identify the nature of the QCD transition in a realistic simulation scenario.

YiLun Du, Kai Zhou, Jan Steinheimer, LongGang Pang, Anton Motornenko, HongShi Zong, XinNian Wang, Horst Stöcker
Nucl.Phys.A 1005 (2021) 121891
ePrint: 2009.03059 [nuclth]

The possibility of twin star solutions in a model based on lattice QCD thermodynamics
Abstract
The properties of compact stars and in particular the existence of twin star solutions are investigated within an effective model that is constrained by lattice QCD thermodynamics. The model is modified at large baryon densities to incorporate a large variety of scenarios of first order phase transitions to a phase of deconfined quarks. This is achieved by matching two different variants of the bag model equation of state, in order to estimate the role of the Bag model parameters on the appearance of a second family of neutron stars. The produced sequences of neutron stars are compared with modern constrains on stellar masses, radii, and tidal deformability from astrophysical observations and gravitational wave analyses. It is found that most of the possible scenarios disfavor a strong phase transition to quark matter and do not support the conjecture of a second family of neutron stars.

P. Jakobus, A. Motornenko, R.O. Gomes, J. Steinheimer, H. Stoecker
Eur.Phys.J.C 81 (2021) 41
ePrint: 2004.07026 [nuclth]

QCD equation of state at vanishing and high baryon density: Chiral Mean Field model
Abstract
The thermodynamic properties of high temperature and high density QCDmatter are studied using the Chiral SU(3)flavor paritydoublet Polyakovloop quarkhadron meanfield model, CMF. The CMF model provides a proper description of lattice QCD data, heavyions physics, and static neutron stars. The behavior of lines of constant pressure with increase of baryon density is discussed. The rapid change of pressure behavior at $\mu_B/T\approx3$ suggests a strong contribution of baryons to thermodynamic properties at this region. The position of this region is very close to the radius of convergence for a Taylor expansion of the QCD pressure. The role of mesons and unstable hadrons in the hydrodynamic expansion of strongly interacting matter is also discussed.

Anton Motornenko, Jan Steinheimer, Volodymyr Vovchenko, Stefan Schramm, Horst Stoecker
Nucl.Phys.A 1005 (2021) 121836
ePrint: 2002.01217 [hepph]

Identifying the nature of the QCD transition in relativistic collision of heavy nuclei with deep learning
Abstract
Using deep convolutional neural network (CNN), the nature of the QCD transition can be identified from the finalstate pion spectra from hybrid model simulations of heavyion collisions that combines a viscous hydrodynamic model with a hadronic cascade "afterburner". Two different types of equations of state (EoS) of the medium are used in the hydrodynamic evolution. The resulting spectra in transverse momentum and azimuthal angle are used as the input data to train the neural network to distinguish different EoS. Different scenarios for the input data are studied and compared in a systematic way. A clear hierarchy is observed in the prediction accuracy when using the eventbyevent, cascadecoarsegrained and eventfineaveraged spectra as input for the network, which are about 80%, 90% and 99%, respectively. A comparison with the prediction performance by deep neural network (DNN) with only the normalized pion transverse momentum spectra is also made. Highlevel features of pion spectra captured by a carefullytrained neural network were found to be able to distinguish the nature of the QCD transition even in a simulation scenario which is close to the experiments.

YiLun Du, Kai Zhou, Jan Steinheimer, LongGang Pang, Anton Motornenko, HongShi Zong, XinNian Wang, Horst Stöcker
Eur.Phys.J.C 80 (2020) 516
ePrint: 1910.11530 [hepph]

Phase Transitions and Bose–Einstein Condensation in AlphaNucleon Matter
Abstract
The equation of state and the phase diagram of an isospinsymmetric chemically equilibrated mixture of a particles and nucleons (N) are studied in the meanfield approximation. We use a Skyrmelike parametrization of meanfield potentials as functions of the partial densities of particles. The parameters of these potentials are chosen by fitting the known properties of pure N and pure amatters at zero temperature. The sensitivity of results to the choice of the aN attraction strength is investigated. The phase diagram of the a − N mixture is studied with a special attention paid to the liquidgas phase transitions and the Bose–Einstein condensation of a particles. We have found two firstorder phase transitions, stable and metastable, which differ significantly by the fractions of a’s. It is shown that the states with a condensate are metastable.

L.M. Satarov, I.N. Mishustin, A. Motornenko, V. Vovchenko, M.I. Gorenstein, H. Stoecker
Ukr.J.Phys. 64 (2019)

Kinetic freezeout temperature from yields of shortlived resonances
Abstract
A method to determine the kinetic freezeout temperature in heavyion collisions from measured yields of shortlived resonances is presented. The resonance production is treated in the framework of thermal model with an evolution between chemical and kinetic freezeouts. The yields of many shortlived resonances are suppressed at $T = T_{\rm kin} < T_{\rm ch}$. We determine the values of $T_{\rm kin}$ and $T_{\rm ch}$ for various centralities in PbPb collisions at $\sqrt{s_{_{NN}}} = 2.76$ TeV by fitting the abundances of both the stable hadrons and the shortlived resonances such as $\rho^0$ and $ \text{K}^{*0}$, that were measured by the ALICE collaboration. This allows to extract the kinetic freezeout temperature from the measured hadron and resonance yields alone, independent of assumptions about the flow velocity profile and the freezeout hypersurface. The extracted $T_{\rm ch}$ values exhibit a moderate multiplicity dependence whereas $T_{\rm kin}$ drops, from $T_{\rm kin} \simeq T_{\rm ch} \simeq 155$ MeV in peripheral collisions to $T_{\rm kin} \simeq 110$ MeV in 020% central collisions. Predictions for other shortlived resonances are presented. A potential (non)observation of a suppressed $f_0(980)$ meson yield will allow to constrain the lifetime of that meson.

Anton Motornenko, Volodymyr Vovchenko, Carsten Greiner, Horst Stoecker
Phys.Rev.C 102 (2020) 024909
ePrint: 1908.11730 [hepph]

Detecting the HadronQuark Phase Transition with Gravitational Waves
Abstract
The longawaited detection of a gravitational wave from the merger of a binary neutron star in August 2017 (GW170817) marks the beginning of the new field of multimessenger gravitational wave astronomy. By exploiting the extracted tidal deformations of the two neutron stars from the late inspiral phase of GW170817, it is now possible to constrain several global properties of the equation of state of neutron star matter. However, the most interesting part of the high density and temperature regime of the equation of state is solely imprinted in the postmerger gravitational wave emission from the remnant hypermassive/supramassive neutron star. This regime was not observed in GW170817, but will possibly be detected in forthcoming events within the current observing run of the LIGO/VIRGO collaboration. Numerous numericalrelativity simulations of merging neutron star binaries have been performed during the last decades, and the emitted gravitational wave profiles and the interior structure of the generated remnants have been analysed in detail. The consequences of a potential appearance of a hadronquark phase transition in the interior region of the produced hypermassive neutron star and the evolution of its underlying matter in the phase diagram of quantum cromo dynamics will be in the focus of this article. It will be shown that the different density/temperature regions of the equation of state can be severely constrained by a measurement of the spectral properties of the emitted postmerger gravitational wave signal from a future binary compact star merger event.

Matthias Hanauske, Luke Bovard, Elias Most, Jens Papenfort, Jan Steinheimer, et al.
Universe 5 (2019) 156

Backward nucleon production by heavy baryonic resonances in protonnucleus collisions
Abstract
The production of backward nucleons, $N(180^\circ)$, at $180^\circ$ in the nuclear target rest frame in protonnucleus ($\mathrm{p}+A$) collisions is studied. The backward nucleons appearing outside of the kinematically allowed range of protonnucleon ($\mathrm{p}+N$) reactions are shown to be due to secondary reactions of heavy baryonic resonances produced inside the nucleus. Baryonic resonances $R$ created in primary $\mathrm{p}+N$ reactions can change their masses and momenta due to successive collisions $R+N\rightarrow R +N $ with other nuclear nucleons. Two distinct mechanisms and kinematic restrictions are studied: the reaction $R+N\rightarrow N(180^\circ)+N$ and the resonance decay $R\rightarrow N(180^\circ)+\pi$. Simulations of $\mathrm{p}+A$ collisions using the Ultrarelativistic Quantum Molecular Dynamics model support these mechanisms and are consistent with available data on proton backward production.

Oleksandra Panova, Anton Motornenko, Mark I. Gorenstein, Jan Steinheimer, Horst Stoecker
Phys.Rev.C 100 (2019) 054617
ePrint: 1908.01365 [nuclth]

MAGIC  how MAtter’s extreme phases can be revealed in Gravitational wave observations and in relativistic heavy Ion Collision experiments
Abstract
Nearly one hundred years after Albert Einstein developed the field equations of general relativity and predicted the existence of gravitational waves, a gravitational wave event from a binary neutron star merger (GW170817) was detected in August 2017 by the LIGO/VIRGO collaboration. During the thereon analysis of the gravitational wave data, the equation of state of elementary matter could be constrained in the regime of high densities/temperatures. Recent simulations show, that the appearance of a hadron to quark phase transition in the interior region of a hybrid star merger remnant might change the overall properties of the merger event and could be detectable in future. On the one hand, 4Dsimulations of binary neutron star mergers show that these astrophysical systems represent optimal laboratories to investigate the phase structure of quantum chromodynamics. On the other hand, accelerators like the FAIR facility at GSI Helmholtzzentrum allow one to study the properties of the quarkgluon plasma produced in relativistic collisions of heavy ions. This article combines a survey of recent advancements in two rather distinct fields, which reveal  on first sight  a surprising similarity of both, namely relativistic collisions of nuclei and of neutron star mergers.

Matthias Hanauske, Luke Bovard, Jan Steinheimer, Anton Motornenko, Volodymyr Vovchenko, et al.
J.Phys.Conf.Ser. 1271 (2019) 012023

Matter And Gravitation In Collisions of heavy ions and neutron stars: equation of state
Abstract
The gravitational waves emitted from a binary neutron star merger, as predicted from general relativistic magnetohydrodynamics calculations, are sensitive to the appearance of quark matter and the stiffness of the equation of state of QCD matter present in the inner cores of the stars. This is a new messenger observable from outer space, which does provide direct signals for the phase structure of strongly interacting QCD matter at high baryon density and high temperature. These astrophysically created extremes of thermodynamics do match, to within 20\%, the values of densities and temperatures which we find in relativistic hydrodynamics and transport theory of heavy ion collisions at the existing laboratories, if though at quite different rapidity windows, impact parameters and bombarding energies of the heavy nuclear systems. We demonstrate how one unified equation of state can be constructed and used for both neutron star physics and hot QCD matter excited at laboratory facilities. The similarity in underlying QCD physics allows the gravitational wave signals from future advanced LIGO and Virgo events to be combined with the analysis of high multiplicity fluctuations and flow measurements in heavy ion detectors in the lab to pin down the EoS and the phase structure of dense matter.

Anton Motornenko, Jan Steinheimer, Volodymyr Vovchenko, Stefan Schramm, Horst Stoecker
PoS CORFU2018 (2019) 150
ePrint: 1907.05921 [hepph]

Chemical freezeout conditions and fluctuations of conserved charges in heavyion collisions within quantum van der Waals model
Abstract
The chemical freezeout parameters in central nucleusnucleus collisions are extracted consistently from hadron yield data within the quantum van der Waals (QvdW) hadron resonance gas model. The beam energy dependences for skewness and kurtosis of net baryon, net electric, and net strangeness charges are predicted. The QvdW interactions in asymmetric matter, $Q/B \neq 0.5$, between (anti)baryons yield a noncongruent liquidgas phase transition, together with a nuclear critical point (CP) with critical temperature of $T_c=19.5$ MeV. The nuclear CP yields the collision energy dependence of the skewness and the kurtosis to both deviate significantly from the ideal hadron resonance gas baseline predictions even far away, in $(T,\mu_B)$plane, from the CP. These predictions can readily be tested by STAR and NA61/SHINE Collaborations at the RHIC BNL and the SPS CERN, respectively, and by HADES at GSI. The results presented here offer a broad opportunity for the search for signals of phase transition in dense hadronic matter at the future NICA and FAIR high intensity facilities.

R. Poberezhnyuk, V. Vovchenko, A. Motornenko, M.I. Gorenstein, H. Stoecker
Phys.Rev.C 100 (2019) 054904
ePrint: 1906.01954 [hepph]

Equation of state for hot QCD and compact stars from a mean field approach
Abstract
The thermodynamic properties of high temperature and high density QCDmatter are explored within the Chiral SU(3)flavor paritydoublet Polyakovloop quarkhadron meanfield model, CMF. The quark sector of the CMF model is tuned to describe the $\mu_B=0$ thermodynamics data of lattice QCD. The resulting lines of constant physical variables as well as the baryon number susceptibilities are studied in some detail in the temperature/chemical potential plane. The CMF model predicts three consecutive transitions, the nuclear firstorder liquidvapor phase transition, chiral symmetry restoration, and the crossover transition to a quarkdominated phase. All three phenomena are crossover, for most of the $T\mu_B$plane. The deviations from the free ideal hadron gas baseline at $\mu_B=0$ and $T\approx 100200$ MeV can be attributed to remnants of the liquidvapor first order phase transition in nuclear matter. The chiral crossing transition determines the baryon fluctuations at much higher $\mu_B\approx1.5$ GeV, and at even higher baryon densities $\mu_B\approx2.4$ GeV, the behavior of fluctuations is controlled by the deconfinement crossover. The CMF model also describe well the static properties of high $\mu_B$ neutron stars as well as the new neutron star merger observations. The effective EoS presented here describes simultaneously lattice QCD results at $\mu_B=0$, as well as observed physical phenomena (nuclear matter and neutron star matter) at $T\cong0$ and high densities, $\mu_B>1$ GeV.

Anton Motornenko, Jan Steinheimer, Volodymyr Vovchenko, Stefan Schramm, Horst Stoecker
Phys.Rev.C 101 (2020) 034904
ePrint: 1905.00866 [hepph]

The analytic structure of thermodynamic systems with repulsive interactions
Abstract
Thermodynamic properties of systems with repulsive interactions, are considered in the grand canonical ensemble. The analytic structure of the excludedvolume model in the complex plane of the system chemical potential (fugacity) is elaborated, based on the fact that the pressure function can be given in terms of the Lambert Wfunction. Even though the excluded volume model has no phase transitions at real values of the chemical potential, it does exhibit a branch cut singularity in the complex plane, thus limiting the convergence range of the Taylor expansion in the chemical potential. Close similarities to analytic properties of the other models with repulsive interactions, such as a cluster expansion model, the meanfield model, and the ideal Fermi gas model, are pointed out. As an example, repulsive baryonic interactions in a hadron gas, with a focus on the fugacity/virial and Taylor expansion methods used in lattice QCD, are presented. The asymptotic behavior of the Fourier expansion coefficients in these various models suggests that the singular part of net baryonic density can to leading order be universally expressed in terms of polylogarithms.

Kirill Taradiy, Anton Motornenko, Volodymyr Vovchenko, Mark I. Gorenstein, Horst Stoecker
Phys.Rev.C 100 (2019) 065202
ePrint: 1904.08259 [hepph]

Neutron Star Mergers: Probing the EoS of Hot, Dense Matter by Gravitational Waves
Abstract
Gravitational waves, electromagnetic radiation, and the emission of high energy particles probe the phase structure of the equation of state of dense matter produced at the crossroad of the closely related relativistic collisions of heavy ions and of binary neutron stars mergers. 3 + 1 dimensional special and general relativistic hydrodynamic simulation studies reveal a unique window of opportunity to observe phase transitions in compressed baryon matter by laboratory based experiments and by astrophysical multimessenger observations. The astrophysical consequences of a hadronquark phase transition in the interior of a compact star will be focused within this article. Especially with a future detection of the postmerger gravitational wave emission emanated from a binary neutron star merger event, it would be possible to explore the phase structure of quantum chromodynamics. The astrophysical observables of a hadronquark phase transition in a single compact star system and binary hybrid star merger scenario will be summarized within this article. The FAIR facility at GSI Helmholtzzentrum allows one to study the universe in the laboratory, and several astrophysical signatures of the quarkgluon plasma have been found in relativistic collisions of heavy ions and will be explored in future experiments.

Matthias Hanauske, Jan Steinheimer, Anton Motornenko, Volodymyr Vovchenko, Luke Bovard, Elias R. Most, L.Jens Papenfort, Stefan Schramm, Horst Stöcker
Particles 2 (2019)

Hadron yields and fluctuations at energies available at the CERN Super Proton Synchrotron: Systemsize dependence from Pb + Pb to $p$+$p$ collisions
Abstract
The kaon to pion ratio $K^+/\pi^+$ and the scaled variance $\omega^$ for fluctuations of negatively charged particles are studied within the statistical hadron resonance gas (HRG) model and the Ultra relativistic Quantum Molecular Dynamics (UrQMD) transport model. The calculations are done for p+p, Be+Be, Ar+Sc, and Pb+Pb collisions at the CERN Super Proton Synchrotron energy range to reveal the system size dependence of hadron production. For the HRG calculations the canonical ensemble is imposed for all conserved charges. In the UrQMD simulations the centrality selection in nucleusnucleus collisions is done by calculating the forward energy $E_{\rm F}$ deposited in the Projectile Spectator Detector, and the acceptance maps of the NA61/SHINE detectors are used. A comparison of the HRG and UrQMD results with the data of the NA61/SHINE Collaboration is done. To understand a difference of the eventbyevent fluctuations in p+p and heavy ion collisions the centrality selection procedure in the sample of all inelastic p+p events is proposed and analyzed within the UrQMD simulations.

A. Motornenko, V.V. Begun, V. Vovchenko, M.I. Gorenstein, H. Stoecker
Phys.Rev.C 99 (2019) 034909
ePrint: 1811.10645 [nuclth]

Phase transitions and BoseEinstein condensation in $\alpha$ nucleon matter
Abstract
The equation of state and phase diagram of isospinsymmetric chemically equilibrated mixture of alpha particles and nucleons are studied in the meanfield approximation. The model takes into account the effects of Fermi and Bose statistics for nucleons and alphas, respectively. We use Skyrmelike parametrization of the meanfield potentials as functions of partial densities, which contain both attractive and repulsive terms. Parameters of these potentials are chosen by fitting known properties of pure nucleon and pure alpha matter at zero temperature. The sensitivity of results to the choice of the alphanucleon attraction strength is investigated. The phase diagram of the alphanucleon mixture is studied with a special attention paid to the liquidgas phase transitions and the BoseEinstein condensation of alpha particles. We have found two firstorder phase transitions, stable and metastable, which differ significantly by the fractions of alpha particles. It is shown that states with alpha condensate are metastable.

L.M. Satarov, I.N. Mishustin, A. Motornenko, V. Vovchenko, M.I. Gorenstein, H. Stoecker
Phys.Rev.C 99 (2019) 024909
ePrint: 1811.02924 [nuclth]

QCD at high density: Equation of state for nuclear collisions and neutron stars
Abstract
A unified chiral mean field approach is presented for QCD thermodynamics in a wide range of temperatures and densities. The model simultaneously gives a satisfactory description of lattice QCD thermodynamics and fulfills nuclear matter and astrophysical constraints. The resulting equation of state can be incorporated in relativistic fluiddynamical simulations of heavyion collisions and neutron stars mergers. Access to different regions of the QCD phase diagram can be obtained in simulations of heavyion data and observations of neutron star mergers.

Anton Motornenko, Volodymyr Vovchenko, Jan Steinheimer, Stefan Schramm, Horst Stoecker
Nucl.Phys.A 982 (2019)
ePrint: 1809.02000 [hepph]

Eventbyevent fluctuations in p+p and central A+A collisions within relativistic transport models
Abstract
Eventbyevent multiplicity fluctuations in nucleusnucleus collisions are studied within the relativistic transport models: EPOS, PHSD, and UrQMD. As measures of particle number fluctuations we consider the scaled variances $\omega[X]$ for positive, negative, and all charged hadrons, and the strongly intensive quantities $\Delta[K^+,\pi^+],$ $\Sigma[K^+,\pi^+]$ for $K^+$ and $\pi^+$ yields. At the SPS energy range the fluctuation measures are calculated for protonproton, Ar+Sc, and Pb+Pb collisions. Comparison with recent NA61/SHINE and older NA49 measurements of the multiplicity fluctuations is done. A validity of the model of independent sources, a role of the experimental acceptance, and the centrality selection procedure are studied.Eventbyevent multiplicity fluctuations in nucleusnucleus collisions are studied within the relativistic transport models: EPOS, PHSD, and UrQMD. As measures of particle number fluctuations we consider the scaled variances $\omega[X]$ for positive, negative, and all charged hadrons, and the strongly intensive quantities $\Delta[K^+,\pi^+],$ $\Sigma[K^+,\pi^+]$ for $K^+$ and $\pi^+$ yields. At the SPS energy range the fluctuation measures are calculated for protonproton, Ar+Sc, and Pb+Pb collisions. Comparison with recent NA61/SHINE and older NA49 measurements of the multiplicity fluctuations is done. A validity of the model of independent sources, a role of the experimental acceptance, and the centrality selection procedure are studied.

Anton Motornenko, Katarzyna Grebieszkow, Elena Bratkovskaya, Mark I. Gorenstein, Marcus Bleicher, Klaus Werner
J.Phys.G 45 (2018) 115104
ePrint: 1711.07789 [nuclth]

Nucleon matter equation of state, particle number fluctuations, and shear viscosity within UrQMD box calculations
Abstract
Properties of equilibrated nucleon system are studied within the Ultrarelativistic Quantum Molecular Dynamics (UrQMD) transport model. The UrQMD calculations are done within a finite box with periodic boundary conditions. The system achieves thermal equilibrium due to nucleonnucleon elastic scattering. For the UrQMD equilibrium state, nucleon energy spectra, equation of state, particle number fluctuations, and shear viscosity $\eta$ are calculated. The UrQMD results are compared with both, statistical mechanics and ChapmanEnskog kinetic theory, for a classical system of nucleons with hardcore repulsion.

A. Motornenko, L. Bravina, M.I. Gorenstein, A.G. Magner, E. Zabrodin
J.Phys.G 45 (2018) 035101
ePrint: 1710.09276 [nuclth]

BethUhlenbeck approach for repulsive interactions between baryons in a hadron gas
Abstract
The quantum mechanical BethUhlenbeck (BU) approach for repulsive hardcore interactions between baryons is applied to the thermodynamics of a hadron gas. The second virial coefficient $a_2$  the "excluded volume" parameter  calculated within the BU approach is found to be temperature dependent, and it differs dramatically from the classical excluded volume (EV) model result. At temperatures $T =100200$ MeV, the widely used classical EV model underestimates the EV parameter for nucleons at a given value of the nucleon hardcore radius by large factors of 34. Previous studies, which employed the hardcore radii of hadrons as an input into the classical EV model, have to be reevaluated using the appropriately rescaled EV parameters. The BU approach is used to model the repulsive baryonic interactions in the hadron resonance gas (HRG) model. Lattice data for the second and fourth order net baryon susceptibilities are described fairly well when the temperature dependent BU baryonic excluded volume parameter corresponds to nucleon hardcore radii of $r_c = 0.250.3$ fm. Role of the attractive baryonic interactions is also considered. It is argued that HRG model with a constant baryonbaryon EV parameter $v_{NN} \simeq 1$ fm$^3$ provides a simple yet efficient description of baryonbaryon interaction in the crossover temperature region.

Volodymyr Vovchenko, Anton Motornenko, Mark I. Gorenstein, Horst Stoecker
Phys.Rev.C 97 (2018) 035202
ePrint: 1710.00693 [nuclth]

Multicomponent van der Waals equation of state: Applications in nuclear and hadronic physics
Abstract
A generalization of the quantum van der Waals equation of state for a multicomponent system in the grand canonical ensemble is proposed. The model includes quantum statistical effects and allows to specify the parameters characterizing repulsive and attractive forces for each pair of particle species. The model can be straightforwardly applied to the description of asymmetric nuclear matter and also for mixtures of interacting nucleons and nuclei. Applications of the model to the equation of state of an interacting hadron resonance gas are discussed.

Volodymyr Vovchenko, Anton Motornenko, Paolo Alba, Mark I. Gorenstein, Leonid M. Satarov, Horst Stoecker
Phys.Rev.C 96 (2017) 045202
ePrint: 1707.09215 [nuclth]

BoseEinstein condensation and liquidgas phase transition in alphamatter
Abstract
Systems of Bose particles with both repulsive and attractive interactions are studied using the Skyrmelike meanfield model. The phase diagram of such systems exhibits two special lines in the chemical potentialtemperature plane: one line which represents the firstorder liquidgas phase transition with the critical end point, and another line which represents the onset of BoseEinstein condensation. The calculations are made for stronglyinteracting matter composed of alpha particles. The phase diagram of this matter is qualitatively similar to that observed for the atomic He4 liquid. The sensitivity of the results to the model parameters is studied. For weak interaction coupling the critical point is located at the Bosecondensation line.

L.M. Satarov, M.I. Gorenstein, A. Motornenko, V. Vovchenko, I.N. Mishustin, H. Stoecker
J.Phys.G 44 (2017) 12
ePrint: 1704.08039 [nuclth]

Cumulative pion production via successive collisions in nuclear medium
Abstract
Production of pions in protonnucleus (p+A) reactions outside of a kinematical boundary of protonnucleon collisions, the socalled cumulative effect, is studied. The kinematical restrictions on pions emitted in backward direction in the target rest frame are analyzed. It is shown that cumulative pion production requires a presence of massive baryonic resonances that are produced during successive collisions of projectile with nuclear nucleons. After each successive collision the mass of created resonance may increase and, simultaneously, its longitudinal velocity decreases. Simulations within Ultra relativistic Quantum Molecular Dynamics model reveals that successive collisions of baryonic resonances with nuclear nucleons plays the dominant role in cumulative pion production in p+A reactions.

A. Motornenko, M.I. Gorenstein
Acta Phys.Polon.Supp. 10 (2017) 681
ePrint: 1610.02950 [nuclth]

Cumulative production of pions by heavy baryonic resonances in protonnucleus collisions
Abstract
Pion production in protonnucleus (p+A) collisions outside the kinematical boundary of protonnucleon (p+N) reactions, the socalled cumulative effect, is studied. Restrictions from energymomentum conservation on the energy of pions emitted in the backward direction in the target rest frame are analyzed. It is assumed that the cumulative pions are produced in p+A reactions by heavy baryonic resonances. The baryonic resonances are first created in p+N reactions. Due to successive collisions with nuclear nucleons the masses of these resonances may then increase and, simultaneously, their longitudinal velocities decrease. We also use the Ultra relativistic Quantum Molecular Dynamics model to reveal the key role of successive collisions of baryonic resonances with nuclear nucleons for cumulative pion production in p+A reactions. Further experimental studies of cumulative hadron production in p+A reactions at high collision energies are needed to search for heavy hadronlike objects and investigate their properties.

A. Motornenko, M.I. Gorenstein
J.Phys.G 44 (2017) 025105
ePrint: 1604.04308 [hepph]