Emergent Dimensions: from Geometry to Topology and Phenomena, Prof. Chia-Yi Ju [朱家誼], NSYSU

Tuesday 14 Apr 2026, 13:30 → 15:30 Asia/Taipei

Physics/124

Recent studies have shown that the Schrödinger equation can be realized geometrically. In this talk, we briefly review some basic ideas in differential geometry and explore their similarities and connections with quantum physics. We then demonstrate how hidden dimensions can emerge naturally from parameter spaces and derive the evolution equations for arbitrary quantum states along these emergent dimensions, as well as the equations governing the fiber metric of the associated Hilbert space bundle. Next, we show how Berry connections relate to the state evolution equations and illustrate that exceptional points act as topological defects in the Hilbert space bundle. Finally, we demonstrate how these concepts relate to the quantum phase transition.