Quantum electrodynamic description of ionization of the neutral hydrogen molecule

We investigate hydrogen molecule ionization within a unified framework combining finite-dimensional quantum electrodynamics with the Lindblad master equation, enabling systematic comparison across closed, dissipative, and influx-driven open systems. Our results reveal a universal tendency toward neutral [Formula: see text] formation. Photon dissipation ([Formula: see text]) accelerates stabilization, while electron ([Formula: see text]) and phonon ([Formula: see text]) dissipation play distinct regulatory roles. Particle influx ([Formula: see text]) induces complex energy redistribution, populating the atomic state [Formula: see text]. The ionization pathway is highly sensitive to initial photon number and composition, which control spin-selective excitation channels. An embedded anode model confirms that orbital hybridization fundamentally constrains the maximum ionization probability to [Formula: see text]. This work provides a unified theoretical foundation for quantum-controlled chemistry and cavity QED experiments.