Electric field induction in quark-gluon plasma due to thermoelectric effects

Relativistic heavy-ion collisions produce quark-gluon plasma (QGP), which is locally thermalized. Due to electrically charged particles (quarks), QGP exhibits interesting thermoelectric phenomena during its evolution, resulting in an electromagnetic (EM) field in the medium. In this study, for the first time, we estimate the induced electric field in QGP due to the thermoelectric effect. This phenomenon can induce an EM field even in QGP produced by the head-on heavy-ion collision. In peripheral heavy-ion collisions, the presence of a spectator current generates a transient magnetic field at the early stage, which disrupts the isotropy of the induced electric field. For the numerical estimation, we use a quasiparticle-based model that incorporates the lattice quantum chromodynamics equation of state for QGP. The induced electric field is estimated with cooling rates derived from Gubser hydrodynamic flow. Thermoelectric coefficients such as Seebeck, magneto-Seebeck, and Nernst coefficients play a crucial role in determining the induced field. Additionally, we account for the temperature evolution of QGP using different hydrodynamic cooling rates to calculate the transport coefficients. We also estimate the transport coefficients and the induced electric field in the presence of an external time-varying magnetic field, including the quantum effect of Landau quantization, and explore the effects of the intensity and decay parameter of the magnetic field on the induced electric field. Our findings reveal that the space-time profile of the induced electric field is zero at the center and increases as we go away from the center. During the early stages of evolution, the electric field can reach a maximum value of $eE \approx 1~m_\pi^2$, decreasing in strength over time.