Description
Recent studies have demonstrated that the Schrödinger equation can be realized geometrically. In this talk, we explore the role of differential geometry in non-Hermitian quantum physics. We then demonstrate how hidden dimensions naturally emerge from parameter spaces, examining their relation to Berry connections and curvatures. Finally, we highlight unexpected topological structures residing within these parameter spaces.
References:
[1] Jen-Yin Yeh and Chia-Yi Ju, "Evolution Generators for Complex Parameters," arXiv: 2608.29602 (2026).
[2] C.-Y. Ju, S.-M. Chen,"Evidence for Exceptional Points as Topological Defects, "arXiv:2412.06548 [Quantum, to be published (2026)].
[3] C.-Y. Ju, A. Miranowicz, Y.-N. Chen, G.-Y. Chen, F. Nori, "Emergent Parallel Transports and Curvatures in Non-Hermitian Quantum Mechanics," Quantum 8, 1277 (2024).
[4] C.-Y. Ju, A. Miranowicz, G.-Y. Chen, F. Nori, "Non-Hermitian Hamiltonians and no-go theorems in quantum information," Phys. Rev. A 100, 062118 (2019).