Surface trapping and Auger recombination typically suppress the emission of quantum dots (QDs). Understanding how these two processes affect the emission properties of QDs is critical to optimizing their photoluminescence (PL) performance. However, isolating their respective contributions can be challenging. In this study, we investigate the respective effects of surface trapping and Auger recombination on QD emission using single QD spectroscopy. The effects of surface trapping and Auger recombination on QD emission can be distinguished by analyzing the real-time changes in the radiative and non-radiative rates of the PL trajectories of single QDs. This is because Auger recombination can alter both the radiative and non-radiative rates, while surface trapping changes only the non-radiative rate. We find that when the PL trajectory of a single QD is in a gray state due to surface trapping, it can still exhibit Auger blinking induced by charging. Surface trapping introduces non-radiative recombination pathways not only for neutral exciton states but also for trion states. This further confirms that surface trapping and Auger recombination in QDs are completely independent non-radiative pathways. The ability to distinguish the respective effects of Auger recombination and surface trapping provides valuable insights into QD emission mechanisms.

First, we investigate the trade-off relations of quantum battery capacities in two-qubit system. We find that the sum of subsystem battery capacity is governed by the total system capacity, with this trade-off relation persisting for a class of Hamiltonians, including Ising, XX, XXZ and XXX models. Then building on this relation, we define residual battery capacity for general quantum states and establish coherent/incoherent components of subsystem battery capacity. Furthermore, we introduce the protocol to guide the selection of appropriate incoherent unitary operations for enhancing subsystem battery capacity in specific scenarios, along with a sufficient condition for achieving subsystem capacity gain through unitary operation. Numerical examples validate the feasibility of the incoherent operation protocol. Additionally, for the three-qubit system, we also established a set of theories and results parallel to those for two-qubit case. Finally, we determine the minimum time required to enhance subsystem battery capacity via a single incoherent operation in our protocol. Our findings contribute to the development of quantum battery theory and quantum energy storage systems.