XXV DAE-BRNS High Energy Physics Symposium 2022

Study of chiral dependent charge and heat conductivity and their associated numbers in thermal QCD

16 Dec 2022, 14:00

1h

LHC Foyer (IISER Mohali)

Poster Poster - 4

Speaker

pushpa panday

Description

As the strength of the magnetic field ($𝐵$) becomes weak, novel phenomena,
similar to the Hall effect in condensed matter physics
emerges both in charge and heat transport in a thermal
QCD medium with a finite quark chemical potential ($\mu$).
So we have calculated the transport coefficients
in a kinetic theory within a quasiparticle framework,
wherein we compute the effective mass of quarks for the
aforesaid medium in a weak magnetic field (B) limit
($|eB|$< QCD up to one loop, which depends on $𝑇$ and $𝐵$ differently to
left- ($L$) and right-handed ($R$) chiral modes of quarks, lifting
the prevalent degeneracy in $L$ and $R$ modes in a strong magnetic field
limit ($|𝑒𝐵|>>{𝑇}^2$). Another implication of weak
$𝐵$ is that the transport coefficients assume a tensorial structure:
The diagonal elements represent the usual (electrical and thermal)
conductivities: ${\sigma }_{\text{Ohmic}}$ and ${\kappa }_0$ as the
coefficients of charge and heat transport, respectively
and the off-diagonal elements denote their Hall counterparts:
${\sigma }_{\text{Hall}}$ and ${\kappa }_1$, respectively.
It is found in charge transport that the magnetic field acts on
$L$- and $R$-modes of the Ohmic-part of electrical conductivity in
opposite manner, viz. ${\sigma }_{\text{Ohmic}}$ for $L$- mode decreases
and for $R$- mode increases with $𝐵$ whereas the Hall-part ${\sigma }_{\text{Hall}}$
for both $L$- and $R$-modes always increase with $𝐵$.
In heat transport too, the effect of the magnetic field on the usual thermal
conductivity (${\kappa }_0$) and Hall-type coefficient (${\kappa }_1$) in both
modes are identical to the abovementioned effect of $𝐵$ on charge
transport coefficients.

We have then derived some coefficients from the above transport
coefficients, namely Knudsen number ($\mathrm{\Omega }$ is the ratio of
the mean free path to the length scale of the system)
and Lorenz number in Wiedemann-Franz law. The effect of $𝐵$ on $\mathrm{\Omega }$
either with ${\kappa }_0$ or with ${\kappa }_1$ for both modes are identical to
the behavior of ${\kappa }_0$ and ${\kappa }_1$ with 𝐵. The value of
$\mathrm{\Omega }$ is always less than unity for the entire temperature range,
validating our calculations. Lorenz number (${\kappa }_0$/${\sigma }_{\text{Ohmic}}𝑇$) and
Hall-Lorenz number (${\kappa }_1$/${\sigma }_{\text{Hall}}𝑇$) for $L$-mode
decreases and for $R$-mode increases with a magnetic
field. It also does not remain constant with $T$, except for
the $R$-mode Hall-Lorenz number where it remains almost constant
for smaller values of $B$.