Effect of strong magnetic field on the interplay of momentum, heat and charge transports in a hot QCD matter

Jun 2, 2020, 7:30 AM
1h 20m


Poster Presentation New Theoretical Developments Poster session


Ms Shubhalaxmi Rath (Indian Institute of Technology Roorkee)


We have studied the effect of strong magnetic field on the interplay
of coefficients related to the transports of momentum, heat and
charge of a hot QCD matter by shear ($\eta$) and bulk ($\zeta$)
viscosities, thermal ($\kappa$) and electrical ($\sigma_{\rm el}$)
conductivities, and some derived coefficients,
{\em viz.} $\frac{\eta}{s}$, $\frac{\zeta}{s}$, Lorenz (L), Knudsen
($\Omega$), Prandtl (Pl), Reynolds (Rl) numbers and ratio of momentum
diffusion to charge diffusion. We have also computed the
abovementioned coefficients in the absence (isotropic) and presence
of momentum anisotropy caused by the asymptotic expansion at the early stages
of ultrarelativistic heavy-ion collisions, which facilitates us to
compare the effects of anisotropies with respect to the isotropic
medium. We have first calculated the
viscosities, conductivities and entropy density ($s$) in the relaxation time approximation of kinetic theory within the quasiparticle model.
Compared to the isotropic medium, both $\eta$ and $\zeta$ get enhanced
in the presence of strong magnetic field, contrary to their
reduction in expansion-driven anisotropy. $\eta$ increases with temperature
faster in the former case than in the latter case, whereas $\zeta$ in the former case decreases with temperature and in the latter case, it is
meagre and vanishes at a specific temperature. We have also observed that
both $\kappa$ and $\sigma_{\rm el}$ get increased in a strong magnetic field,
but $\kappa$ increases slowly with the temperature,
contrary to its rapid increase in expansion-driven anisotropy,
whereas $\sigma_{\rm el}$ monotonically decreases with the temperature,
opposite to the increase in expansion-driven anisotropy. Thus, the
viscosities and conductivities could distinguish the effects of strong
magnetic field and expansion-driven anisotropy. In the presence of
momentum anisotropies, the entropy density gets decreased, especially it
is lowest in the $B$-driven anisotropy due to reduction of
phase-space. Thus, $\eta/s$ gets enhanced in the $B$-driven anisotropy
and in the expansion-driven anisotropy, it becomes
smaller than the isotropic one. Similarly $\zeta/s$ gets amplified but
decreases faster with the temperature in a strong magnetic field. The
value of the Lorenz number, {\em i.e.}, the ratio,
$\kappa/(\sigma_{\rm el}T)$ in $B$-driven anisotropy is larger than in
isotropic medium, but smaller than in expansion-driven
anisotropy. The Knudsen number gets reduced in expansion-driven anisotropy,
whereas the strong magnetic field raises its value but to less than one, thus the system stays in local equilibrium. The Prandtl number
gets increased in $B$-induced anisotropy, whereas it gets decreased in
expansion-induced anisotropy, compared to isotropic one. Since, Pl is
found larger than 1, the sound attenuation is governed by the
momentum diffusion. The strong magnetic field makes the Reynolds number
smaller than one, whereas the expansion-driven anisotropy makes it
larger. Finally the ratio $(\eta/s)/(\sigma_{\rm el}/T)$ is amplified
much in strong magnetic field, whereas the amplification is less
pronounced in the absence of magnetic field. Since, the ratio is found more than one,
so the momentum diffusion prevails over the charge diffusion.

Contribution type Contributed Talk
Track Electroweak Probes

Primary authors

Prof. Binoy Krishna Patra (Indian Institute of Technology Roorkee) Ms Shubhalaxmi Rath (Indian Institute of Technology Roorkee)

Presentation materials