Relativistic Boltzmann Transport Research Articles

Seebeck and Nernst coefficients of a magnetized hot QCD medium with a number conserving kernel

We study the thermoelectric response of a hot and magnetized QCD medium created in the noncentral events at heavy-ion collider experiments. The collisional aspects of the medium have been embedded in the relativistic Boltzmann transport equation (RBTE) using the Bhatnagar-Gross-Krook (BGK) collision integral, which insures the particle number conservation, unlike the commonly used relaxation time approximation (RTA). We have incorporated the thermal medium effects in the guise of a quasiparticle model, where the interaction among the quarks and gluons is assimilated in the medium dependent masses of the quarks, which have been evaluated using imaginary-time formalism of thermal QCD with a background magnetic field. In the absence of $B$, the Seebeck coefficient for individual quark flavors gets slightly reduced in the BGK term in comparison to naive RTA, while it gets enhanced for the composite partonic medium. In the strong magnetic field ($B$), the BGK term enhances the Seebeck coefficient for the individual flavors, as well as that for the medium. The medium Seebeck coefficient rises with the strength of quark chemical potential ($\ensuremath{\mu}$) in the absence, as well as that in the strong $B$. We observe chirality dependence in the transport coefficients in the weak $B$ as the masses of chiral modes become nondegenerate. In the case of the $L$ modes, the BGK collision term causes a slight reduction in the Seebeck coefficient, while for $R$ modes both the collision integrals produce the same results. The Nernst coefficient gets reduced (enhanced) for $L$ ($R$) chiral modes in the BGK term.

Effects of weak magnetic field and finite chemical potential on the transport of charge and heat in hot QCD matter

We have studied the effects of weak magnetic field and finite chemical potential on the transport of charge and heat in hot QCD matter by estimating their respective response functions, viz. the electrical conductivity ( $$\sigma _{\textrm{el}}$$ ), the Hall conductivity ( $$\sigma _{\textrm{H}}$$ ), the thermal conductivity ( $$\kappa _0$$ ) and the Hall-type thermal conductivity ( $$\kappa _1$$ ). The expressions of charge and heat transport coefficients are obtained by solving the relativistic Boltzmann transport equation in the relaxation time approximation at weak magnetic field and finite chemical potential. The interactions among partons are incorporated through their thermal masses. We have observed that $$\sigma _{{\textrm{el}}}$$ and $$\kappa _0$$ decrease and $$\sigma _{{\textrm{H}}}$$ and $$\kappa _1$$ increase with the magnetic field in the weak magnetic field regime. On the other hand, the presence of a finite chemical potential increases these transport coefficients. The effects of weak magnetic field and finite chemical potential on aforesaid transport coefficients are found to be more conspicuous at low temperatures, whereas at high temperatures, they have only a mild dependence on magnetic field and chemical potential. We have found that the presence of finite chemical potential further extends the lifetime of the magnetic field. Furthermore, we have explored the effects of weak magnetic field and finite chemical potential on the Knudsen number, the elliptic flow coefficient and the Wiedemann–Franz law.

Directed flow of D mesons at RHIC and LHC energy within a transport approach: non-perturbative dynamics, vorticity and electromagnetic fields

We study the propagation of charm quarks in the quark-gluon plasma (QGP) by means a relativistic Boltzmann transport (RBT) approach coupled to electromagnetic field. The interplay between these fields is responsible to generate large rapidity odd directed flow v1 of D mesons and for a large splitting of directed flow Δv1 between neutral D and anti-D mesons. We show that the large v1 is generated by the longitudinal asymmetry between the bulk matter and the charm quarks and by a large non-perturbative interaction in the QGP medium.

Thermoelectric transport coefficients of quark matter

A thermal gradient and/or a chemical potential gradient in a conducting medium can lead to an electric field, an effect known as thermoelectric effect or Seebeck effect. In the context of heavy-ion collisions, we estimate the thermoelectric transport coefficients for quark matter within the ambit of the Nambu–Jona Lasinio (NJL) model. We estimate the thermal conductivity, electrical conductivity, and the Seebeck coefficient of hot and dense quark matter. These coefficients are calculated using the relativistic Boltzmann transport equation within relaxation time approximation. The relaxation times for the quarks are estimated from the quark–quark and quark–antiquark scattering through meson exchange within the NJL model. As a comparison to the NJL model estimation of the Seebeck coefficient, we also estimate the Seebeck coefficient within a quasiparticle approach.

Hadron production within a full transport approach with statistical hadronization mechanism at RHIC and LHC energies

We present for the first time results on final hadron production, with and without strangeness content, in Ultrarelativistic Heavy Ion Collisions at RHIC and LHC center of mass energies obtained combining a full 3+1D relativistic Boltzmann transport approach with a statistical hadronization mechanism. The non-perturbative interaction between quarks and gluons is described by means of a quasi-particle approach that permits to have an Equation of State close to lattice QCD. The resulting framework naturally includes both shear and bulk viscous effects. The 3+1D full transport evolution is converted to hadrons by mean of a realistic freeze-out hypersurface considering all known hadron resonances and by performing resonance decays. We present results on charged-hadron multiplicity, identified-particle spectra and identified-particle elliptic flow of π, K and p produced at RHIC and LHC energies for different centralities.

Electromagnetic response of hot QCD medium in the presence of background time-varying fields

The response of the hot QCD medium in the presence of external time dependent electromagnetic fields has been studied within the relativistic Boltzmann transport theory. The impact of the time dependence of the electromagnetic fields and collisional aspects of the medium to the induced electric and Hall current densities has been explored. The non-equilibrium momentum distribution of degrees of freedom has been obtained in the presence of space-time varying electromagnetic fields. Further, the analysis has been extended to an anisotropic QCD medium while incorporating the in-medium interaction effects. It is observed that the electric charge transport is sensitive to the inhomogeneity of the fields and the momentum anisotropy of the QCD medium.

Thermoelectric response of a weakly magnetized thermal QCD medium

We estimate the thermoelectric response, namely, the Seebeck and Nernst coefficients of a hot and deconfined plasma of quarks and gluons, created post ultrarelativistic heavy ion collisions in the presence of a weak, homogeneous background magnetic field. We employ the kinetic theory framework, wherein we use the relativistic Boltzmann transport equation in the relaxation time approximation. In-medium interactions are taken into account via the quasiparticle masses of the partons extracted from one loop perturbative thermal QCD. We calculate the individual and total Seebeck coefficients in 2 different approaches (1-D and 2-D formulations). In the 1-D analysis, we find that a larger current quark mass has an amplifying effect on the individual Seebeck coefficient in the presence of a weak magnetic field. The temperature sensitivities of the individual Seebeck coefficients increase with increase in the current mass of the quark species in the case of a weak magnetic field whereas the same records a decreasing trend in the presence of a strong magnetic field. The variation of individual and total Seebeck coefficients with temperature, chemical potential and background magnetic field are found to follow similar trends in both the approaches, viz. decrease in magnitude with increasing temperature and increase in magnitude with increase in chemical potential and magnetic field. We also calculate the individual and total Nernst coefficients (in 2-D formulation) which are found to decrease with both temperature and chemical potential and increase with the magnetic field. Further, we find that the sign of the Nernst coefficient is independent of the electric charge of the charge carrier of the medium.

Centrality dependence of electrical and Hall conductivity at RHIC and LHC energies for a conformal system

In this work, we study electrical conductivity and Hall conductivity in the presence of electromagnetic field using Relativistic Boltzmann Transport Equation with Relaxation Time Approximation. We evaluate these transport coefficients for a strongly interacting system consisting of nearly massless particles which is similar to Quark-Gluon Plasma and is likely to be formed in heavy-ion collision experiments. We explicitly include the effects of magnetic field in the calculation of relaxation time. The values of magnetic field are obtained for all the centrality classes of Au+Au collisions at $\sqrt {s_{\rm NN}} =$ 200 GeV and Pb+Pb collisions at $\sqrt {s_{\rm NN}} =$ 2.76 TeV. We consider the three lightest quark flavors and their corresponding antiparticles in this study. We estimate the temperature dependence of the electrical conductivity and Hall conductivity for different strengths of magnetic field. We observe a significant dependence of temperature on electrical and Hall conductivity in the presence of magnetic field.

Viscous properties of hot and dense QCD matter in the presence of a magnetic field

We have studied the effect of strong magnetic field on the viscous properties of hot QCD matter at finite chemical potential by calculating the shear viscosity (eta ) and the bulk viscosity (zeta ). The viscosities have been calculated using the relativistic Boltzmann transport equation within the relaxation time approximation. The interactions among partons are incorporated through their quasiparticle masses at finite temperature, strong magnetic field and finite chemical potential. From this study, one can understand the influence of strong magnetic field and the influence of chemical potential on the sound attenuation through the Prandtl number (Pl), on the nature of the flow by the Reynolds number (Rl), and on the relative behavior between the shear viscosity and the bulk viscosity through the ratio zeta /eta . We have observed that, both shear and bulk viscosities get increased in the presence of a strong magnetic field and the additional presence of chemical potential further enhances their magnitudes. With the increase of temperature, eta increases for the medium in the presence of a strong magnetic field as well as for the isotropic medium in the absence of magnetic field, whereas zeta is found to decrease with the temperature, contrary to its increase in the absence of magnetic field. We have observed that, the Prandtl number gets increased in the presence of strong magnetic field and finite chemical potential as compared to that in the isotropic medium, but it always remains larger than unity, thus instead of the thermal diffusion, the momentum diffusion largely affects the sound attenuation in the medium and this is more vigorous in the presence of both strong magnetic field and finite chemical potential. However, the Reynolds number becomes lowered than unity in an ambience of strong magnetic field and even gets further decreased in an additional presence of chemical potential, thus it implies the dominance of kinematic viscosity over the characteristic length scale of the system. Finally, the ratio zeta /eta is amplified to the value larger than unity, contrary to its value in the absence of magnetic field and chemical potential where it is less than unity, thus it is inferred that the bulk viscosity prevails over the shear viscosity for the hot and dense QCD matter in the presence of a strong magnetic field.

Transport properties of Heavy Quarks: anisotropic flows υn and their correlations to the bulk dynamics and initial Electromagnetic field

We study the correlations between light flavor and heavy quarks (HQs) flow harmonics at LHC energy within a transport approach. We have investigated the role of transport coefficient in developing these anisotropic flows correlations. We suggest correlation and the relative fluctuations of anisotropic flows συη /〈υn 〉 as novel observables to constrain the HQ transport coefficients in quark gluon plasma. Finally, very strong electro-magnetic (E.M.) fields are created in Ultra-relativistic Heavy-Ion Collision (HIC). We show within relativistic Boltzmann transport approach coupled with E.M. field that the strong e.m. field is responsible for a splitting of directed flow υ 1 of D and anti-D mesons of few percent, i.e. much larger compared to the observed charged particles. Moreover, we discuss the role played by the initial large bulk vorticity on the build up of rapidity odd HQs directed flow υ 1.

Seebeck effect in a thermal QCD medium in the presence of strong magnetic field

The strongly interacting partonic medium created post ultrarelativistic heavy ion collision experiments exhibits a significant temperature-gradient between the central and peripheral regions of the collisions, which in turn, is capable of inducing an electric field in the medium; a phenomenon known as Seebeck effect. The effect is quantified by the magnitude of the induced electric field per unit temperature-gradient - the Seebeck coefficient ($S$). We study the coefficient, $S$ in the relativistic Boltzmann transport equation in relaxation-time approximation, as a function of temperature ($T$) and chemical potential ($\mu$), wherein we find that with current quark masses, the magnitude of $S$ for individual flavours as well as that for the medium as a whole decreases with $T$ and increases with $\mu$, with the electric charge of the flavour deciding the sign of $S$. The emergence of a strong magnetic field ($B$) in the non-central collisions at heavy-ion collider experiments motivates us to study the effect of $B$ on Seebeck effect. The strong $B$ affects $S$ in multifold ways, via : a) modification of phase-space due to the dimensional reduction, b) dispersion relation in lowest Landau level (occupation probability), and c) relaxation-time. We find that a strong $B$ not only decreases the magnitudes of $S$'s of individual species, it also flips their signs. This leads to a faster reduction of the magnitude of $S$ of the medium than its counterpart at $B=0$. We then explore how the interactions among partons in perturbative thermal QCD in the quasiparticle framework affect Seebeck effect, where we find that even in strong B, there is no more a flip of the sign of $S$ for individual species and an enhancement of the magnitudes of $S$ of individual species as well as that of the medium, compared to current quark mass description at either $B=0$ or $B \neq 0$.

Transport coefficients of hot and dense hadron gas in a magnetic field: A relaxation time approach

We estimate various transport coefficients of hot and dense hadronic matter in the presence of magnetic field. The estimation is done through solutions of the relativistic Boltzmann transport equation in the relaxation time approximation.We have investigated the temperature and the baryon chemical potential dependence of these transport coefficients. Explicit calculations are done for the hadronic matter in the ambit of hadron resonance gas model. We estimate thermal conductivity, electrical conductivity and the shear viscosity of hadronic matter in the presence of a uniform magnetic field. Magnetic field, in general, makes the transport coefficients anisotropic. It is also observed that all the transport coefficients perpendicular to the magnetic field are smaller compared to their isotropic counterpart.

Revisit to electrical and thermal conductivities, Lorenz and Knudsen numbers in thermal QCD in a strong magnetic field

We have explored how the electrical ($\sigma_{\rm el}$) and thermal ($\kappa$) conductivities in a thermal QCD medium get affected in weak-momentum anisotropies arising either due to a strong magnetic field or due to asymptotic expansion. This study facilitates to understand the longevity of strong magnetic field through $\sigma_{el}$, Lorenz number in Wiedemann-Franz law, and the validity of equilibrium by the Knudsen number. We calculate the conductivities by solving relativistic Boltzmann transport equation in relaxation-time approximation within quasiparticle model at finite T and strong B. We have found that $\sigma_{el}$ and $\kappa$ get enhanced in a magnetic field-driven anisotropy, but $\sigma_{el}$ decreases with temperature, opposite to its faster increase in expansion-driven anisotropy. Whereas $\kappa$ increases slowly with temperature, contrary to its rapid increase in expansion-driven anisotropy. The above findings are broadly attributed to three factors: the stretching and squeezing of distribution function in anisotropies generated by the magnetic field and asymptotic expansion, respectively, the dispersion relation and resulting phase-space factor, the relaxation-time in absence and presence of strong magnetic field. So $\sigma_{\rm el}$ extracts the time-dependence of magnetic field, which decays slower than in vacuum but expansion-driven anisotropy makes the decay faster. The variation in $\kappa$ transpires that Knudsen number decreases with T but expansion-driven anisotropy reduces its value and magnetic field-driven anisotropy raises its value but to less than one, thus the system can still be in equilibrium. The ratio, $\kappa/\sigma_{el}$ in magnetic field-driven anisotropy increases linearly with temperature but with a value smaller than in expansion-driven anisotropy. Thus the Lorenz number can make the distinction between different anisotropies.

Transport properties from Charm to Bottom: pT suppression, anisotropic flow νn and their correlations to the bulk dynamics

We study the propagation of heavy quarks (HQs) in the quark-gluon plasma (QGP) by means of a relativistic Boltzmann transport (RBT) approach. The non-perturbative interaction between heavy quarks and light quarks is described by means of a quasi-particle approach able to describe simultaneously the experimental data for the nuclear suppression factor RAA and the elliptic flow ν2(pT) of D mesons from RHIC to LHC energies. In the same framework we predict the B meson nuclear modification factor at LHC. Finally, we discuss the relevance of initial state fluctuations that allows to extend the analysis to high order anisotropic flows νn(pT) as well as to investigate the role of QCD interaction in developing correlations between the light and the heavy flavour anisotropic flows.

Heavy Quark Dynamics toward thermalization: RAA, υ1, υ2, υ3

We describe the propagation of Heavy quarks (HQs) in the quark-gluon plasma (QGP) within a relativistic Boltzmann transport (RBT) approach. The interaction between heavy quarks and light quarks is described within quasi-particle approach which is able to catch the main features of non-perturbative interaction as the increasing of the interaction in the region of low temperature near TC. In our calculations the hadronization of charm quarks in D mesons is described by mean of an hybrid model of coalescence plus fragmentation. We show that the coalescence play a key role to get a good description of the experimental data for the nuclear suppression factor RAA and the elliptic flow υ2(pT) at both RHIC and LHC energies. Moreover, we show some recent results on the direct flow υ1 and triangular flow υ3 of D meson.

Heavy quark dynamics within a Boltzmann transport model: radiative vs collisional energy loss

We discuss the propagation of heavy quarks (charm and bottom) through the QGP by means of a relativistic Boltzmann transport approach including both collisional and radiative energy loss mechanisms. In particular we investigate the impact of induced gluon radiation by dynamical QCD medium implementing in our transport model a formula for the emitted gluon spectrum calculated in a higher-twist scheme. We notice that in the region of high transverse momentum (pT > 10 GeV) radiative processes play an essential role giving a dominant contribution to the generation of RAA and v2 at momentum values for which the energy loss by collisions is in the perturbative regime.

Impact of early stage non-equilibrium dynamics on photon production in relativistic heavy ion collisions

In this study we discuss our results on the spectrum of photons emitted from the quark-gluon plasma produced in heavy ion collisions at RHIC energies. Simulating the space-time evolution of the fireball by solving the relativistic Boltzmann transport equation and including two-particle scattering processes with photon emission allows us to make a first step in the description of thermal photons from the QGP as well as of those produced in the pre-equilibrium stage. Indeed, we consider not only a standard Glauber initial condition but also a model in which quarks and gluons are produced in the very early stage through the Schwinger mechanism by the decay of an initial color-electric field. In the latter approach relativistic kinetic equations are coupled in a self-consistent way to field equations. We aim at spotting the impact of early stage non-equilibrium dynamics on the photon production.

Electric Conductivity of the QGP

The transport coefficients of strongly interacting matter have attracted a great interest in the field of Quark-Gluon Plasma (QGP). In this work we compute electric conductivity σel solving numerically the Relativistic Boltzmann Transport (RBT) equation in a uniform box with periodic boundary conditions considering 2—body scatterings. We compare numerical results obtained using two methods, Green-Kubo correlator and E-field method, with analytic formulas in Relaxation Time Approximation (RTA). We present results for the realistic case of the QGP system considering both a quasi-particle model tuned to lattice QCD thermodynamics as well as the case of a pQCD gas with a running coupling constant. Calculations based on RTA underestimate σel of about 60%.

Relativistic Boltzmann transport approach with Bose-Einstein statistics and the onset of gluon condensation

We study the evolution of a gluon system under conditions of density and temperature similar to those explored in the early stage of ultrarelativistic heavy-ion collisions. We first describe the implementation of the relativistic Boltzmann-Nordheim (RBN) transport approach that includes in the collision integral the quantum effects of Bose-Einstein statistics. Then, we describe the evolution of a spatially uniform gluon system in a box under elastic collisions solving the RBN for various initial conditions. We discuss the critical phase-space density that leads to the onset of a Bose-Einstein condensate (BEC) and the time scale for this process to occur. In particular, thanks to the fact that RBN allows one to relax the small angle approximation, we study the effect at both small and large screening mass ${m}_{D}$. For small ${m}_{D}\ensuremath{\ll}T$ we see that our solution of RBN is in agreement with the recent extensive studies within a Fokker-Planck scheme in small angle approximation. For the same total cross section but with large ${m}_{D}\ensuremath{\simeq}2\phantom{\rule{0.16em}{0ex}}T$ (large angle scatterings), we see a significant time speed-up of the onset of BEC with respect to small ${m}_{D}\ensuremath{\ll}T$. This further strengthens the possibility that at least a transient BEC is formed in the early stage of ultrarelativistic heavy-ion collisions.

Time dependence of partition into spectators and participants in relativistic heavy-ion collisions

The process of formation of the participant system in heavy-ion collisions is investigated in the framework of a simplified analytic Glauber-like model, which is based on the relativistic Boltzmann transport equation. The key point lies in the time-dependent partition of the nucleon system into two groups: nucleons, which did not take part in any interaction before a given time, and nucleons, which already have interacted. In the framework of the proposed model we introduce a natural energy-dependent temporal scale ${t}_{c}$, which allows us to remove all dependencies of the model on the collision energy except for the energy dependence of the nucleon-nucleon cross section. By investigating the time dependence of the total number of participants we conclude that the formation process of the participant system becomes complete at $t\ensuremath{\simeq}1.5{t}_{c}$. Time dependencies of participant total angular momentum and vorticity are also considered and used to describe the emergence of rotation in the reaction plane.