While stated that the bonuses do not stack with themselves, that is not entirely true. When the bonus AP granted by Living Battery interacts with ability power modifiers, such as Rabadon's Deathcap or Archmage, the bonus AP gained from those modifiers triggers more mana from Living Battery. This creates a cyclic loop. The same is also true for maximum mana modifiers, such as Expanded Mind.
Toggle: Dialmond surround itself with a maelstrom of pure energy, dealing magic damage every half seconds to enemies nearby. 15% of the damage done to champions are transform into a shield for Dialmond, with each instance lasting up to 3 seconds.