What flows in the chiral magnetic effect? -- Simulating the particle production with CP-breaking backgrounds

To address a question of whether the chiral magnetic current is a static polarization or a genuine flow of charged particles, we elucidate the numerical formulation to simulate the net production of right-handed particles and anomalous currents with CP-breaking background fields which cause an imbalance between particles and anti-particles. For a concrete demonstration we numerically impose pulsed electric and magnetic fields to confirm our answer to the question that the produced net particles flow in the dynamical chiral magnetic effect. The rate for the particle production and the chiral magnetic current generation is quantitatively consistent with the axial anomaly, while they appear with a finite response time. We emphasize the importance to quantify the response time that would suppress observable effects of the anomalous current.