Dynamical Electromagnetic fields and Dynamical Electromagnetic Anomaly in heavy ion collisions at intermediate energies

Electromagnetic field produced in non-central heavy ion collisions play a crucial role in phenomena such as chiral anomalous effects, directed flow of mesons and splitting of spin polarization of $\Lambda/\bar{\Lambda}$. A precise description of these fields is essential for quantitatively studying these effects. We investigate the space-time evolution of the electromagnetic fields by numerically solving Maxwell's equations using the results from the UrQMD model, rather than relying on an ansatz. We present the space-averaged dynamic electromagnetic fields, weighted by energy density, in the central region of heavy-ion collisions. These measurements can serve as a barometer for assessing the effects induced by magnetic fields. Comparing the fields at geometric center of the collisions, the space-averaged dynamical fields weighted by the energy density are smaller at the early stage but damp much slower at the later stage. We discuss the impact of these space averaged dynamical magnetic fields on the spin polarization and spin alignment in heavy ion collisions. Additionally, we explore the opportunity to study non-perturbative regime of Quantum Electrodynamics (QED) by presenting the simulation results for space averaged dynamical electric field at intermediate collision energies. Finally, the space-averaged dynamical electromagnetic anomaly $\boldsymbol{\textbf{E}}$$\cdot\boldsymbol{\textbf{B}}$ weighted by energy density is also calculated and compared with experimentally measured slope parameter $r$.