Wigner function formalism and the evolution of thermodynamic quantities in an expanding magnetized plasma

Abstract

By combining the Wigner function formalism of relativistic quantum kinetic theory with fundamental equations of relativistic magnetohydrodynamics (MHD), we present a novel approach to determine the proper time evolution of the temperature and other thermodynamic quantities in a uniformly expanding hot, magnetized, and weakly interacting plasma. The aim is to study the contribution of quantum corrections to this evolution. We first determine the corresponding Wigner function in terms of the solution of the Dirac equation in the presence of a constant magnetic field. Using this function, we then compute the energy-momentum tensor of the above-mentioned plasma, which eventually yields its energy density and pressure. Plugging these quantities in the energy equation of relativistic MHD, we arrive, after choosing an appropriate coordinate system, at a differential equation for the temperature as a function of the proper time. The numerical solution of this equation leads finally to the proper time evolution of the temperature. The latter is then used to determine the evolution of a large number of thermodynamic quantities in this expanding and magnetized plasma. We compare our results with other existing results from relativistic MHD. We also comment on the effect of point to point decaying magnetic fields on the thermodynamic properties of this plasma.

Thermoelectric transport coefficients of quark matter

“…Electrical conductivity (σ el ) [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32] is also important as the heavy-ion collisions may be associated with large electromagnetic fields. The magnetic field produced in non-central collisions has been estimated to be of the order of ∼ m 2 π at RHIC energy scales [33][34][35][36][37][38][39][40]. Such magnetic fields are amongst the strongest magnetic fields produced in nature and can affect various properties of the strongly interacting medium.…”

Role of Time-Varying Magnetic Field on QGP Equation of State

“…So, the LLL approximation is physically the most suitable and widely employed by several authors in strong magnetic fields [55][56][57][58], while the contributions from the highest Landau levels are difficult to estimate [59][60][61][62] in such field limits. Recently, an interesting work has been done by Tabatabaee and Sadooghi who have used the Wigner function formalism and evaluated the thermodynamic quantities in an expanding magnetized plasma incorporating the quantum effects arising from the Landau quantization [63].…”

Thermoelectric transport coefficients of quark matter

“…Electrical conductivity (σ el ) [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32] is also important as the heavy-ion collisions may be associated with large electromagnetic fields. The magnetic field produced in non-central collisions has been estimated to be of the order of ∼ m 2 π at RHIC energy scales [33][34][35][36][37][38][39][40]. Such magnetic fields are amongst the strongest magnetic fields produced in nature and can affect various properties of the strongly interacting medium.…”