In quantum mechanics, the geometry of quantum states has emerged as a powerful framework for understanding phenomena ranging from electrical conductivity to superconductivity. One research direction aims to extend these geometric concepts to non-Hermitian quantum mechanics—where systems can exchange energy with their environment—including the generalization of the Berry phase, a key geometric quantity, to the non-Hermitian case.

However, many geometric properties unique to non-Hermitian quantum mechanics remain poorly understood.

“We knew geometry played a central role in ordinary quantum mechanics, but what genuinely new geometric effects might emerge in the non-Hermitian case was far from clear,” explains Tomoki Ozawa, a theoretical physicist at AIMR. “We wanted to identify geometric phenomena that are truly intrinsic to non-Hermitian quantum mechanics.”