Dynamic Calculations of Magnetic Field and Implications on Spin Polarization and Spin Alignment in Heavy Ion Collisions

Magnetic field plays a crucial role in various novel phenomena in heavy-ion collisions. We solve the Maxwell equations numerically in a medium with time-dependent electric conductivity by using the Finite-Difference Time-Domain (FDTD) algorithm. We investigate the time evolution of magnetic fields in two scenarios with different electric conductivities at collision energies ranging from $\sqrt{s_{\text{NN}}}=$ 7.7 to 200 GeV. Our results suggest that the magnetic field may not persist long enough to induce a significant splitting between the global spin polarizations of $\mathrm{\Lambda }$ and $\bar{\mathrm{\Lambda }}$ at freeze-out stage. However, our results do not rule out the possibility of the magnetic field influencing the spin (anti-)alignment of vector mesons.