One particle distribution function and shear viscosity in magnetic field: A relaxation time approach

Mohanty, P. K.; Dash, Ashutosh; Roy, Victor

doi:10.1140/epja/i2019-12705-7

Cited by 44 publications

(34 citation statements)

References 54 publications

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“…( 36) and ( 37) for Scalar and Dirac particle respectively. Relaxation time approximation (RTA) of kinetic theory provide the form of conductivity in terms of relaxation time as [12,17,35,37] Scalar,Dirac =…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

“…Thus the different components of conductivity are obtained by application of the corresponding projectors on the conductivity tensor . In RTA [12,17], it is found that electrical conductivity breaks up into multiple components with respect to the direction of the external magnetic field. In our Kubo formalism, the different components of conductivities are obtain from…”

Section: Electrical Conductivity From Spectral Function In Kubo Forma...mentioning

confidence: 99%

“…Their microscopic estimations become quite important as they enter as input of evolving QGP. Based on that interest, microscopic calculations of transport coefficients like shear viscosity [9][10][11][12][13][14][15][16][17], bulk viscosity [18][19][20][21][22] and electrical conductivity [12,[23][24][25][26][27][28][29][30][31][32][33][34][35] for the relativistic systems in presence of magnetic field are rigorously studied in recent time. Relaxation time appoximation (RTA) of kinetic theory and Kubo formalism are the two frequently used approaches for microscopic calculation of transport coefficients.…”

Section: Introductionmentioning

confidence: 99%

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Kubo estimation of the electrical conductivity for a hot relativistic fluid in the presence of a magnetic field

Satapathy,

Ghosh,

Ghosh

2021

Preprint

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We have explored the multi-component structure of electrical conductivity of relativistic Fermionic and Bosonic fluid in presence of magnetic field by using Kubo approach. This is done by explicitly evaluating the thermo-magnetic vector current spectral functions using the real time formalism of finite temperature field theory and the Schwinger proper time formalism. In absence of magnetic field, the one-loop diagramatic representation of Kubo expression of any transport coefficients is exactly same with relaxation time approximation (RTA) based expression, but this equality does not hold for finite magnetic field picture due to lacking of proper implementation of quantum effect in latter approach. We have shown this discrepancy for particular transport coefficient -electrical conductivity, whose starting point in Kubo approach will be electromagnetic currentcurrent correlator and its one-loop skeleton diagram carrying two scalar/Dirac propagators for scalar/Dirac fluid. Through a numerical comparison between RTA and Kubo expressions of conductivity components (parallel and perpendicular), we have attempted to interpret detail quantum field theoretical effect, contained by Kubo expression but not by RTA expression. In classical RTA expression we get magnetic field independent parallel conductivity due to zero Lorentz force but in field theoretical Kubo expression, it decreases and increases with the magnetic field for scalar and Dirac medium respectively due to Landau quantization effect. This parallel component of conductivity can be interpreted as zero momentum limit of quantum fluctuation with same Landau level internal lines. While for perpendicular component of conductivity, fluctuation with Landau level differences ±1 are noticed, which might be a new realization of transportation in field theoretical sector.

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Section: Numerical Results and Discussionmentioning

confidence: 99%

Section: Electrical Conductivity From Spectral Function In Kubo Forma...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Kubo estimation of the electrical conductivity for a hot relativistic fluid in the presence of a magnetic field

Satapathy,

Ghosh,

Ghosh

2021

Preprint

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“…Given one uses the same basis as ref. [1], we get the following relations between the transport coefficients [82]:…”

Section: Jhep03(2021)216mentioning

confidence: 99%

Relativistic non-resistive viscous magnetohydrodynamics from the kinetic theory: a relaxation time approach

Panda

Dash

Biswas

et al. 2021

J. High Energ. Phys.

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We derive the relativistic non-resistive, viscous second-order magnetohydrodynamic equations for the dissipative quantities using the relaxation time approximation. The Boltzmann equation is solved for a system of particles and antiparticles using Chapman-Enskog like gradient expansion of the single-particle distribution function truncated at second order. In the first order, the transport coefficients are independent of the magnetic field. In the second-order, new transport coefficients that couple magnetic field and the dissipative quantities appear which are different from those obtained in the 14-moment approximation [1] in the presence of a magnetic field. However, in the limit of the weak magnetic field, the form of these equations are identical to the 14-moment approximation albeit with different values of these coefficients. We also derive the anisotropic transport coefficients in the Navier-Stokes limit.

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“…Moreover, λ and ξ are the effective temperature and anisotropy parameters, that are, in contrast to λ 0 and ξ 0 from previous section, affected by the dissipation of the fluid. To determine δ f d , we follow the method that has been used in [9]. We use rank-two tensors…”

Section: Pos(confinement2018)259mentioning

confidence: 99%

Proper time evolution of magnetic susceptibility in amagnetized plasma of quarks and gluons

Tabatabaee¹,

Sadooghi²

2019

Proceedings of XIII Quark Confinement and the Hadron Spectrum — PoS(Confinement2018)

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In ultrarelativistic heavy ion collisions, enormous magnetic fields are generated because of fastmoving charged particles. In the presence of these magnetic fields, the spin of particles is aligned either in the parallel or in the antiparallel direction with respect to the direction of the magnetic field. A finite magnetization is thus produced. It is known that a finite magnetic susceptibility, χ m , changes the evolution of the energy density of the quark-gluon plasma (QGP), which is believed to be created in these collisions. Depending on whether the system under consideration is a paramagnetic (χ m > 0) or diamagnetic (χ m < 0) fluid, it slows down or speeds up the decay of the energy density, and affect other thermodynamic quantities. In general, one expects that the magnetic susceptibility depends on the magnetic field and temperature. Bearing in mind that these parameters evolve with the evolution of the fluid, a nonuniform magnetic susceptibility in this system is thus expected. In this work, we first determine χ m by using a certain analogy to the standard anisotropic kinetic theory, where the one-particle distribution function is replaced by the corresponding anisotropic distribution function. We then determine the proper time dependence of the magnetic susceptibility in the framework of ideal magnetohydrodynamics. We also study the effect of dissipation on the evolution of χ m .

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One particle distribution function and shear viscosity in magnetic field: A relaxation time approach

Cited by 44 publications

References 54 publications

Kubo estimation of the electrical conductivity for a hot relativistic fluid in the presence of a magnetic field

Kubo estimation of the electrical conductivity for a hot relativistic fluid in the presence of a magnetic field

Relativistic non-resistive viscous magnetohydrodynamics from the kinetic theory: a relaxation time approach

Proper time evolution of magnetic susceptibility in amagnetized plasma of quarks and gluons

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