Shear viscosity 
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 to electrical conductivity 
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>σ</mml:mi></mml:mrow><mml:mrow><mml:mtext>el</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:math>
 ratio for an anisotropic QGP

Thakur, Lata; Srivastava, P. K.; Kadam, Guruprasad; George, Manu; Mishra, Hari Niwas

doi:10.1103/physrevd.95.096009

Cited by 46 publications

(71 citation statements)

References 107 publications

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“…Thus, the QGP is thought to be a viscous medium and the flow remains laminar. Similarly in the calculations using the relativistic kinetic theory [31] and the Chapman-Enskog method with effective fugacity approach [61], the ratio γ ¼ ðη=sÞ=ðσ el =TÞ is reported between 1 to 20 or even higher for a QGP system near transition temperature and gets saturated at higher temperatures.…”

Section: Introductionmentioning

confidence: 72%

“…A variety of calculations on shear and bulk viscosities have been done by applying the perturbation theory [26][27][28], the kinetic theory [29][30][31], and so on for a thermal medium of quarks and gluons in the absence of a magnetic field. In the presence of a magnetic field the rotational invariance is broken, which in turn induces an azimuthal anisotropy of produced particles.…”

Section: Introductionmentioning

confidence: 99%

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Momentum and its affiliated transport coefficients for hot QCD matter in a strong magnetic field

Rath

Patra

2020

Phys. Rev. D

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We have studied the effects of anisotropies on the momentum transport in a strongly interacting matter by the transport coefficients, viz. shear (η) and bulk (ζ) viscosities. The anisotropies could arise either by the strong magnetic field or by the preferential expansion, both of which are created in the very early stages of ultrarelativistic heavy ion collisions at the RHIC or the LHC. This study is thereby aimed to understand (i) the fluidity and location of the transition point of the matter through η=s and ζ=s (s is the entropy density), respectively, (ii) the sound attenuation through the Prandtl number (Pl), (iii) the nature of the flow by the Reynolds number (Rl), and (iv) the competition between momentum and charge diffusions through the ratio ðη=sÞ=ðσ el =TÞ. For this purpose, we have first calculated the viscosities in the relaxation-time approximation of kinetic theory approach and the interactions among partons are embodied by assigning masses to quarks and gluons at finite temperature and strong magnetic field, known as the quasiparticle model. Compared to the isotropic medium, both η and ζ get increased in the magnetic field-driven (B-driven) anisotropy, contrary to the decrease in the expansion-driven anisotropy. Zooming in, η increases with temperature faster in the former case than in the latter case, whereas ζ in the former case monotonically decreases with the temperature and in the latter case, it is meager and ultimately diminishes at a specific temperature. Thus, the behaviors of shear and bulk viscosities could in principle distinguish the aforesaid anisotropies. As a result, η=s gets enhanced in the former case but decreases with temperature and in the latter case, it becomes even smaller than the isotropic one. Similarly, ζ=s gets amplified but decreases faster with the temperature in the presence of a strong magnetic field. The Prandtl number gets increased in B-induced anisotropy and gets decreased in expansion-induced anisotropy, compared to the isotropic case. However, Pl is always found larger than 1, so the sound attenuation is mostly governed by the momentum diffusion. The momentum anisotropy due to the magnetic field makes the Reynolds number smaller than 1, whereas the expansion-driven anisotropy makes it larger. Finally the ratio ðη=sÞ=ðσ el =TÞ is amplified much in the presence of magnetic field-driven anisotropy, whereas the amplification is less pronounced in an isotropic medium as well as in an expansion-driven anisotropic medium. However, the ratio is always more than 1, so the momentum diffusion always prevails over the charge diffusion.

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Section: Introductionmentioning

confidence: 72%

Section: Introductionmentioning

confidence: 99%

Momentum and its affiliated transport coefficients for hot QCD matter in a strong magnetic field

Rath

Patra

2020

Phys. Rev. D

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“…Transport coefficients such as electrical conductivity and thermal conductivity of a hot QCD system can be determined using different models and approaches namely relativistic Boltzmann transport equation [38,[46][47][48], the Chapman-Enskog approximation [45,49], the correlator technique using Green-Kubo formula [18,50,51], and the lattice simulation [52][53][54]. However, we will employ the relativistic Boltzmann transport equation with the relaxation-time approximation to calculate the electrical conductivity for both isotropic and anisotropic hot QCD mediums in Secs.…”

Section: Electrical Conductivitymentioning

confidence: 99%

“…Recently, one of us had observed the effect of this kind of anisotropy on the properties of heavy quarkonium bound states [36] and the electrical conductivity [37], where the heavy quarkonia are found to dissociate earlier than its counterpart in isotropic one and the electrical conductivity decreases with the increase of anisotropy. Later its relation with the shear viscosity was explored in [38]. Besides the abovementioned anisotropies, the event-by-event fluctuations of heavy ion collisions also produce the anisotropy, which plays a crucial role in understanding new phenomena such as the elliptic flow, the triangular flow [39,40] etc.…”

Section: Introductionmentioning

confidence: 99%

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

Rath

Patra

2019

Phys. Rev. D

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We have explored how the electrical (σ el ) and thermal (κ) 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 in a particular direction. This study, in turn, facilitates to understand the longevity of strong magnetic field through σ el , Lorenz number in Wiedemann-Franz law, and the validity of local equilibrium by the Knudsen number through κ. We calculate the conductivities by solving the relativistic Boltzmann transport equation in relaxation-time approximation, where the interactions are incorporated through the distribution function within the quasiparticle approach at finite T and strong B. However, we also compare with the noninteracting scenario, which gives unusually large values, thus validating the quasiparticle description. We have found that both σ el and κ get enhanced in a magnetic field-driven anisotropy, but σ el monotonically decreases with the temperature, opposite to the faster increase in the expansion-driven anisotropy. Whereas κ increases very slowly with the temperature, contrary to its rapid increase in the expansion-driven anisotropy. Therefore, the conductivities may distinguish the origin of anisotropies. The above findings are broadly attributed to three factors: the stretching and squeezing of the distribution function due to the momentum anisotropies generated by the strong magnetic field and asymptotic expansion, respectively, the dispersion relation and the resulting phase-space factor, the relaxation-time in the absence and presence of strong magnetic field. Thus, σ el extracts the time-dependence of initially produced strong magnetic field, which expectedly decays slower than in vacuum but the expansion-driven anisotropy makes the decay faster. The variation in κ transpires that the Knudsen number (Ω) decreases with the temperature, but the expansion-driven anisotropy reduces its magnitude, and the strong magnetic field-driven anisotropy raises its value but to less than one, thus the system can still be in local equilibrium in a range of temperature and magnetic field. Finally, the ratio, κ=σ el in Wiedemann-Franz law in magnetic field-driven anisotropy increases linearly with temperature but its magnitude is smaller than in expansiondriven anisotropic medium. Thus, the slope, i.e., the Lorenz number can make the distinction between the anisotropies of different origins.

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“…The recent studies of the specific shear viscosity of the QGP with N f = 2 + 1 are performed in the phenomenological models, describing QCD matter in terms of the quasiparticle excitations [22][23][24][25][26]. In these models, the essential physics of strong interactions is accommodated into the thermodynamics via an effective coupling and dynamically generated masses depending on temperature T and chemical potential µ.…”

Section: Introductionmentioning

confidence: 99%

Shear viscosity to electrical conductivity ratio in the quasiparticle models

Mykhaylova

2020

Eur. Phys. J. Spec. Top.

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We examine the temperature dependence of the shear viscosity η to electrical conductivity σ ratio, as well as the specific shear viscosity and the scaled electrical conductivity in QCD with light and strange quarks. Our calculations are performed in kinetic theory under the relaxation time approximation combined with the quasiparticle model. We compute all transport parameters using the isotropic and transport cross sections and compare our results to a class of quasiparticle models for the QGP with Nf = 2 + 1. The results depending on different schemes are examined. The ratio (η∕s)∕(σ∕T) quantifies the relation between the relaxation times of gluons and quarks and specifies their comparative role in the evolution of the QGP. We find an excellent agreement with the (η∕s)∕(σ∕T) ratio deduced from the dynamical quasiparticle model in which the quasiparticles are characterized not only by their effective masses but also by finite widths.

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Shear viscosity η to electrical conductivity σel ratio for an anisotropic QGP

Cited by 46 publications

References 107 publications

Momentum and its affiliated transport coefficients for hot QCD matter in a strong magnetic field

Momentum and its affiliated transport coefficients for hot QCD matter in a strong magnetic field

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

Shear viscosity to electrical conductivity ratio in the quasiparticle models

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