Stabilizing ergotropy in Spin-Chain Quantum Batteries via Energy-Invariant Catalysis under Strong Non-Markovian Coupling

Quantum batteries (QBs) have emerged as promising platforms for microscale energy storage, yet most existing studies assume weak system-environment coupling and Markovian dynamics. Here we explore how physical catalysis can regulate the maximum extractable work (ergotropy) of a spin-chain QB strongly coupled to a cavity environment. We model the system using a Nakajima-Zwanzig-type non-Markovian master equation and simulate the time evolution of ergotropy under various physical parameters. Our results show that increasing the catalyst-spin coupling, spin energy or cavity frequency can effectively suppress ergotropy oscillations and yield quasi-stationary ergotropy regime, while overly strong catalyst, especially when accompanied by increasing system-environment coupling under such conditions, can destabilize work extraction. This study demonstrates how quantum catalysis can serve as a control knob for optimizing battery performance in strongly coupled non-Markovian regimes.