RQC Seminar

135th RQC Seminar

  • Speaker

    Prof. Chia-Yi Ju
    ( Department of Physics, National Sun Yat-Sen University, Taiwan )

  • Date

    16:00-17:00, August 7, 2024 (Wednesday)

  • Venue

    Onsite( Wako Main Research 3F 345-347 Seminar Room/ 研究本館3階 セミナー室(345-347) C01）

  • Title

    A Geometric Approach to Quantum Mechanics and its Applications

  • Inquiries

    rqc_info[at]ml.riken.jp

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 Schr¨odinger-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.

References:
[1] 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).
(URL: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.100.062118)
[2] Y.-C. Tzeng, C.-Y. Ju, G.-Y. Chen, W.-M. Huang, “Hunting for the non-Hermitian exceptional points with fidelity susceptibility,” Phy. Rev. Research 3, 013015 (2021).
(URL: https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.3.013015)
[3] C.-Y. Ju, A. Miranowicz, F. Minganti, C.-T. Chan, G.-Y. Chen, F. Nori, “Einstein’s quantum elevator: Hermitization of non-Hermitian Hamiltonians via a generalized vielbein formalism,” Phy. Rev. Research 4, 023070 (2022).
(URL: https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.4.023070)
[4] 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).
(URL: https://quantum-journal.org/papers/q-2024-03-13-1277)
[5] C.-Y. Ju, F.-H. Huang, G.-Y. Chen, “Event-Horizon-Like Singularities and Quantum Phase Transitions,” arXiv:2403.16503 (2024).
(URL: https://arxiv.org/abs/2403.16503)



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