We estimate dissipative properties, viz., shear and bulk viscosities of hadronic matter using relativistic Boltzmann equation in relaxation time approximation within the framework of excluded-volume hadron resonance gas (EHRG) model. We find that at zero baryon chemical potential the shear viscosity to entropy ratio ($\eta /s$) decreases with temperature while at finite baryon chemical potential this ratio shows the same behavior as a function of temperature but reaches close to the Kovtun-Son-Starinets (KSS) bound. Further along the chemical freezeout curve, ratio $\eta /s$ is almost constant apart from small initial monotonic rise. This observation may have some relevance to the experimental finding that the differential elliptic flow of charged hadrons does not change considerably at lower center-of-mass energy. We further find that bulk viscosity to entropy density ($\zeta /s$) decreases with temperature while this ratio has higher value at finite baryon chemical potential at higher temperature. Along the freezeout curve $\zeta /s$ decreases monotonically at lower center-of-mass energy and then saturates.

We study the effect of a strong constant magnetic field, generated in relativistic heavy ion collisions, on the heavy quark complex potential. We work in the strong magnetic field limit with the lowest Landau level approximation. We find that the screening of the real part of the potential increases with the increase in the magnetic field. Therefore, we expect less binding of the $Q\overline{Q}$ pair in the presence of a strong magnetic field. The imaginary part of the potential increases in magnitude with the increase in magnetic field, leading to an increase of the width of the quarkonium state with the magnetic field. All of these effects result in the early dissociation of $Q\overline{Q}$ states in a magnetized hot quark-gluon plasma medium.

We estimate various transport coefficients of hot and dense hadronic matter in the presence of magnetic field. The estimation is done through solutions of the relativistic Boltzmann transport equation in the relaxation time approximation. We have investigated the temperature and the baryon chemical potential dependence of these transport coefficients. Explicit calculations are done for the hadronic matter in the ambit of hadron resonance gas model. We estimate thermal conductivity, electrical conductivity, and the shear viscosity of hadronic matter in the presence of a uniform magnetic field. Magnetic field, in general, makes the transport coefficients anisotropic. It is also observed that all the transport coefficients perpendicular to the magnetic field are smaller compared to their isotropic counterpart.

We estimate the electrical conductivity and the Hall conductivity of a hot and dense hadron gas using the relaxation time approximation for the solution of the Boltzmann transport equation in the presence of an electromagnetic field. We investigate the temperature and the baryon chemical potential dependence of these transport coefficients in the presence of a magnetic field. The explicit calculation is performed within the ambit of the hadron resonance gas model. In general, it is observed that the electrical conductivity decreases in the presence of a magnetic field. While at vanishing magnetic field the electrical conductivity decreases monotonically with temperature, in the presence of a magnetic field the same shows a nonmonotonic behavior with a peak. The Hall conductivity, on the other hand, shows a nonmonotonic behavior with respect to the dependence on a magnetic field as well as with temperature. We argue that for a pair plasma (particle-antiparticle plasma) where ${\mu }_B=0$, Hall conductivity vanishes. Only for a nonvanishing baryon chemical potential, Hall conductivity has a nonzero value. We also estimate the electrical conductivity and the Hall conductivity as a function of the center of mass energy along the freeze-out curve as may be relevant for relativistic heavy-ion collision experiments.

We investigate chiral symmetry breaking in strong magnetic fields at finite temperature and densities in a 3 flavor Nambu Jona Lasinio model including the Kobayashi Maskawa 't Hooft determinant term, using an explicit structure for the ground state in terms of quark-antiquark condensates. The mass gap equations are solved self consistently and are used to compute the thermodynamic potential. We also derive the equation of state for strange quark matter in the presence of strong magnetic fields which could be relevant for proto-neutron stars.