B. Kerbikov, M. Andreichikov
Fermion currents in dense quark matter embedded into magnetic field are under intense discussions motivated by Chiral Magnetic Effect. We argue that conductivity of quark matter may be independent of the magnetic field direction and not proportional to the magnetic field strength.
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We estimate here the electrical and Hall conductivity using a quasiparticle approach for quark matter. We use a Boltzmann kinetic approach in presence of external magnetic field. We confront the results of model calculations with Lattice QCD simulations for vanishing magnetic field. In general electrical conductivity decreases with magnetic field. The Hall conductivity on the other hand can show a non monotonic behaviour with magnetic field due to an intricate interplay of behaviour of relaxation time and strength of the magnetic field. We argue for vanishing quark chemical potential Hall cond…
We have calculated electrical conductivity in the presence of a magnetic field by using the Nambu-Jona-Lasinio model.
We estimate the electrical conductivity and the Hall conductivity of hot and dense hadron gas using the relaxation time approximation of the Boltzmann transport equation in the presence of electromagnetic field. We have investigated the temperature and the baryon chemical potential dependence of these transport coefficients in presence of magnetic field. The explicit calculation is performed within the ambit of the hadron resonance gas model. We find that the electrical conductivity decreases in the presence of magnetic field. The Hall conductivity on the other hand shows a non monotonic behav…
Effect of quantum chromodynamics (QCD) interaction in quark-gluon plasma on electrical conductivity is studied, where lattice quantum chromodynamics (LQCD) results are mapped through quark and gluon degeneracy.
The study of transport coefficients of strongly interacting matter got impetus after the discovery of perfect fluid ever created at ultrarelativistic heavy ion collision experiments. In this article, we have calculated one such coefficient viz. electrical conductivity of the quark gluon plasma (QGP) phase which exhibits a momentum anisotropy. Relativistic Boltzmann's kinetic equation has been solved in the relaxation-time approximation to obtain the electrical conductivity. We have used the quasiparticle description to define the basic properties of QGP. We have compared our model results with…
Electrical conductivity of QGP with quasiparticle quarks and Gribov gluon
本研究采用含Gribov胶子传播子的非微扰重求和与准粒子方法，通过相对论玻尔兹曼方程计算QGP电导率，结果与格点数据高度吻合。
The electromagnetic response of an interacting system of pions has been studied at finite temperature. The corresponding transport parameter i.e. electrical conductivity has been estimated by solving the relativistic transport equation in presence of a finite electric field employing the Chapman-Enskog technique where the collision term has been treated in the relaxation time approximation. The scattering amplitudes of charged pions modeled by $ρ$ and $σ$ meson exchange using an effective Lagrangian have been obtained at finite temperature by introducing self-energy corrections in the thermal …
Effect of chiral imbalance on the electrical conductivity of hot and dense quark matter using Green-Kubo Method within the 2-flavour gauged NJL model
本文在2味规范NJL模型中引入手征化学势，利用Green-Kubo方法和有限温度场论计算了热且密集夸克物质的电导率，发现电导率与温度的比值在低温区显著依赖于手征化学势。
We studied the effect of a strong magnetic field ($B$) on the electrical conductivity of hot quark matter. The electrical conductivity is a key transport coefficient determining the time dependence and strength of magnetic fields generated in a relativistic heavy-ion collision. A~magnetic field induces Hall anisotropic conduction, phase-space Landau-level quantization and, if sufficiently strong, interferes with prominent QCD phenomena such as dynamical quark mass generation, likely affecting the quark matter electrical conductivity, which depends strongly on the quark masses. To address these…
Electromagnetic current-current correlators in pionic and nucleonic medium have been evaluated in the static limit to obtain electrical conductivities for pion and nucleon components respectively, where former decreases and latter one increases with the variation of temperature $T$ and baryon chemical potential $μ_N$. Therefore, total electrical conductivity of pion and nucleon system exhibits a valley structure in the $T$-$μ_N$ plane. To get non-divergent and finite values of correlators, finite thermal widths of medium constituents, pion and nucleon have been considered, where these thermal …
Motivated by the theory of relativistic hydrodynamic fluctuations we make use of the Green-Kubo formula to compute the electrical conductivity and the (second-order) relaxation time of the electric current of an interacting hadron gas. We use the recently developed transport code SMASH to numerically solve the coupled set of Boltzmann equations implementing realistic hadronic interactions. In particular, we explore the role of the resonance lifetimes in the determination of the electrical relaxation time. As opposed to a previous calculation of the shear viscosity we observe that the presence …
We study the Ward identity for the effective photon-electron vertex summing the ladder diagrams contributing to the electrical conductivity in hot QED at leading logarithmic order. It is shown that the Ward identity requires the inclusion of a new diagram in the integral equation for the vertex that has not been considered before. The real part of this diagram is subleading and therefore the final expressions for the electrical conductivity at leading logarithmic order are not affected.
Electrical conductivity and shear viscosity of a pion gas in a thermo-magnetic medium
本文利用动理学理论与弛豫时间近似，计算了热磁介质中相互作用pion气的电导率与剪切粘度，发现介质依赖的散射截面显著影响输运性质。
The electrical conductivity in the hot phase of the QCD plasma is extracted from a quenched lattice measurement of the Euclidean time vector correlator for 1.5 < T/T_c < 3. The spectral density in the vicinity of the origin is examined using a method specially adapted to this region, and a peak at small energies is seen. The continuum limit of the electrical conductivity, and the closely related soft photon emissivity of the QCD plasma, are then extracted from a fit to the Fourier transform of the temporal vector correlator.
A lattice calculation is presented for the electrical conductivity of the QCD plasma with 2+1 dynamical flavours at nonzero temperature. We employ the conserved lattice current on anisotropic lattices using a tadpole-improved clover action and study the behaviour of the conductivity over a wide range of temperatures, both below and above the deconfining transition. The conductivity is extracted from a spectral-function analysis using the Maximal Entropy Method and a discussion of its systematics is provided.
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 $\…
We compute the electrical conductivity ($ σ_{el} $) in the presence of constant and homogeneous external electromagnetic field for the static quark-gluon plasma (QGP) medium, which is among the important transport coefficients of QGP. We present the derivation of the electrical conductivity by solving the relativistic Boltzmann kinetic equation in the relaxation time approximation in the presence of magnetic field ($ B $). We investigate the dependence of electrical conductivity on the temperature and finite chemical potential in magnetic field. We find that electrical conductivity decreases w…
We examine nature of longitudinal electrical conductivity in magnetized electron-ion plasma in the context of binary neutron star mergers. In presence of strong magnetic field, high density and temperature, quantum oscillatory behaviour for electrons emerge due to breakdown of the classical description. For pronounced thermodynamic effects, we consider zeroth Landau level population of electrons for electrical conductivity. We solve Boltzmann equation in presence of magnetic field to obtain the dissipative component of the conductivity. The conductivity is formulated considering dynamically sc…
In this article we study the electrical conductivity in QED using the resummed 3PI effective action. We work to 3-loop order in the effective action. We show that the resulting expression for the conductivity is explicitly gauge invariant, and that the integral equations that resum the pinching and colinear contributions are produced naturally by the formalism. All leading order terms are included, without the need for any kind of power counting arguments.
Electrical conductivity in the early universe
我们数值求解玻尔兹曼方程在早期宇宙中存在一个恒定的电场，并发现电导率$σ$的范围$1\MeV\lsim T\lsim M_W$。对$σ$的主要贡献是由于轻子相互作用。对于$T\lsim 100\MeV$，我们得到$σ\simeq 0.76T$，而对于$T\simeq M_W$，我们得到$σ\simeq 6.7T$
In this article we calculate the electrical conductivity in QED using the 2PI effective action. We use a modified version of the usual 2PI effective action which is defined with respect to self-consistent solutions of the 2-point functions. We show that the green functions obtained from this modified effective action satisfy ward identities and that the conductivity obtained from the kubo relation is gauge invariant. We work to 3-loop order in the modified 2PI effective action and show explicitly that the resulting expression for the conductivity contains the square of the amplitude that corre…
I describe the lattice determination of the electrical conductivity of the quark gluon plasma. Since this is the first extraction of a transport coefficient with a degree of control over errors, I next use this to make estimates of other transport related quantities using simple kinetic theory formulae. The resulting estimates are applied to fluctuations, ultra-soft photon spectra and the viscosity. Dimming of ultra-soft photons is exponential in the mean free path, and hence is a very sensitive probe of transport.
Fluid dynamic considerations are used to determine the electric current spectral density in the regime of small energies and momenta. The spectral density in this regime is parameterized by the electric conductivity, the charge susceptibility, and the relaxation time for the electric current, which is needed for relativistic causality. Experimentally, the spectral function can be accessed through the production rates of photons and dileptons in the expanding quark-gluon plasma. We use fluid dynamic simulations of high energy nuclear collisions, together with the transport limit of the spectral…
We study the transport properties of strongly interacting matter in the context of ultrarelativistic heavy ion collision experiments. We calculate the transport coefficients viz. shear viscosity ($η$) and electrical conductivity ($σ_{\rm{el}}$) of the quark-gluon plasma phase in the presence of momentum anisotropy arising from different expansion rates of the medium in longitudinal and transverse direction. We solve the relativistic Boltzmann kinetic equation in relaxation time approximation to calculate the shear viscosity and electrical conductivity. The calculations are performed within the…
Recently, transport coefficients viz. shear viscosity, electrical conductivity etc. of strongly interacting matter produced in heavy-ion collisions have drawn considerable interest. We study the normalised electrical conductivity ($σ_{\rm el}$/T) of hot QCD matter as a function of temperature (T) using the Color String Percolation Model (CSPM). We also study the temperature dependence of shear viscosity and its ratio with electrical conductivity for the QCD matter. We compare CSPM estimations with various existing results and lattice Quantum Chromodynamics (lQCD) predictions with (2+1) dynamic…
Effect of the Coriolis force on the electrical conductivity of quark matter: A nonrelativistic description
本文在非相对论框架下仅考虑科里奥利力，利用弛豫时间近似玻尔兹曼方程计算旋转夸克物质的电导率，揭示其与磁场中洛伦兹力情形的数学等价性，为后续相对论推广奠定基础。
We have pointed out the possibility of quantum Hall effect or quantum patterns of transportation in a degenerate strongly magnetized quark matter, which might be expected inside a highly dense compact star. An anisotropic pattern of electrical conductivity and resistivity tensor in classical and quantum cases is explored by considering cyclotron motion and Landau quantization respectively. With increasing magnetic field, classical to quantum transitions are realized through enhanced/reduced resistivity/conductivity with jumping pattern. Considering QCD relaxation time scale of 10 fm, $eB\appro…
We investigate the electrical conductivity(EC) of dense quark matter in the vicinity of the phase transition line. We show that: (i) At high density the Drude EC does not depend on the magnetic field up to $eB \sim 10^{19} \ G$. (ii) In the precritical region the fluctuation EC (paraconductivity) dominates over the Drude one.
We investigate the electrical conductivity (sigma) of quark matter via the Kubo formula at finite temperature and zero quark density (T>0, mu=0) in the presence of an external strong magnetic field. For this purpose, we employ the dilute instanton-liquid model, taking into account its temperature modification with the trivial-holonomy caloron distribution. By doing that, the momentum and temperature dependences for the effective quark mass and model renormalization scale are carefully evaluated. From the numerical results, it turns out that sigma\approx(0.02 ~ 0.15)/fm for T=(0 ~ 400) MeV with…
In lattice QCD, the Maximum Entropy Method can be used to reconstruct spectral functions from euclidean correlators obtained in numerical simulations. We show that at finite temperature the most commonly used algorithm, employing Bryan's method, is inherently unstable at small energies and give a modification that avoids this. We demonstrate this approach using the vector current-current correlator obtained in quenched QCD at finite temperature. Our first results indicate a small electrical conductivity above the deconfinement transition.
Extending our recent work, we report on a calculation of the vector current correlation function for light valence quarks in the deconfined phase of quenched QCD in the temperature range 1.16Tc<T<2.98Tc. After performing a systematic analysis of the in fluence of cut-off effects on light quark meson correlators using clover improved Wilson fermions, we discuss resulting constraints on the electrical conductivity in a quark gluon plasma.
By subtracting from a recent lattice measurement of the thermal vector-current correlator the known 5-loop vacuum contribution, we demonstrate that the remainder is small and shows no visible short-distance divergence. It can therefore in principle be subjected to model-independent analytic continuation. Testing a particular implementation, we obtain estimates for the flavour-diffusion coefficient (2 pi T D \gsim 0.8) and electrical conductivity which are significantly smaller than previous results. Although systematic errors remain beyond control at present, some aspects of our approach could…
We report on a continuum extrapolation of the vector current correlation function for light valence quarks in the deconfined phase of quenched QCD. This is achieved by performing a systematic analysis of the influence of cut-off effects on light quark meson correlators at $T\simeq 1.45 T_c$ using clover improved Wilson fermions. We discuss resulting constraints on the electrical conductivity and the thermal dilepton rate in a quark gluon plasma. In addition new results at 1.2 and 3.0 $T_c$ will be presented.
We calculate the electrical conductivity in the early universe at temperatures below as well as above the electroweak vacuum scale, $T_c\simeq 100$GeV. Debye and dynamical screening of electric and magnetic interactions leads to a finite conductivity, $σ_{el}\sim T/α\ln(1/α)$, at temperatures well below $T_c$. At temperatures above, $W^\pm$ charge-exchange processes -- analogous to color exchange through gluons in QCD -- effectively stop left-handed charged leptons. However, right-handed leptons can carry current, resulting in $σ_{el}/T$ being only a factor $\sim \cos^4θ_W$ smaller than at tem…
We present new results on the continuum extrapolation of the vector current correlation function in the deconfined phase for three temperatures close to the critical temperature utilizing quenched clover improved Wilson fermions and light quark masses. A systematic analysis on multiple lattice spacing allows to perform the continuum limit of the correlation function and to extract spectral properties in the continuum limit. These results provide constraints for the electrical conductivity and the thermal dilepton rates in the quark gluon plasma for the given temperature range. In addition resu…
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