Speaker
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
($|eB|<
left- (L) and right-handed (R) chiral modes of quarks, lifting
the prevalent degeneracy in L and R modes in a strong magnetic field
limit ($|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: $\sigma_{\rm Ohmic}$ and $\kappa_0$ as the
coefficients of charge and heat transport, respectively
and the off-diagonal elements denote their Hall counterparts:
$\sigma_{\rm Hall}$ 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. $\sigma_{\rm Ohmic}$ for L- mode decreases
and for R- mode increases with $B$ whereas the Hall-part $\sigma_{\rm Hall}$
for both L- and R-modes always increases 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 ($\Omega$ 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 $\Omega$
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
$\Omega$ 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.
