| Time：1131001 (Tues.) 12:00~14:00 Speaker：朱家誼Chia-Yi Ju Assistant Professor, Department of Physics, National Sun Yat-sen University Title：A Geometric Approach to Quantum Mechanics and its Applications Abstract：It is well-known that quantum states can be interpreted as vectors in a Hilbert space. Nevertheless, the conventional Hilbert space treatment is incompatible with non-Hermitian quantum systems. A natural way to accommodate non-Hermitian quantum systems is to relax the geometry of the Hilbert space from a rigid complex Euclidean space to a Schroedinger-equation-compatible one. In this talk, we start with the motivation and how quantum physics relates to differential geometry. Then we move on to discuss how the (parameter-space-induced) emergent dimensions appear in quantum physics. Finally, we will discuss applications of the emergent dimensions, such as a perturbation method for non-Hermitian systems, some properties of exceptional points in non-Hermitian quantum systems, and a new perspective on quantum phase transitions, even at the Hermitian level. Place：F104, Gongguan Campus, NTNU |
