Electric, thermal, and thermoelectric response of a hot pion gas in a time dependent background magnetic field

In this work, we investigate the electric, thermal, and thermoelectric response of a hot pion gas in the presence of a time-dependent background electromagnetic field. Using the relativistic Boltzmann equation within the relaxation time approximation, we evaluate the Ohmic and Hall conductivities, thermal and Hall-like thermal conductivities, and the magneto-Seebeck and Nernst coefficients, explicitly incorporating the effects of the magnetic field’s strength and decay dynamics. Unlike earlier studies restricted to static fields, our analysis accounts for the temporal evolution of the background magnetic field, capturing the nontrivial time dependence of transport coefficients and their sensitivity to the field profile. We further examine the elliptic flow coefficient, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msub> <a:mi>v</a:mi> <a:mn>2</a:mn> </a:msub> </a:math> , linked to the Knudsen number through the thermal conductivity, and demonstrate its dependence on both the magnitude and decay of the magnetic field. This work provides the first systematic study of pion transport in a realistic, time-varying electromagnetic background and underscores the importance of including such effects in modeling the late stages of heavy-ion collisions at the Relativistic Heavy Ion Collider (RHIC) and LHC.