Interferometric Geometric Phases of $\mathcal{PT}$-symmetric Quantum Mechanics
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arXiv
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| Auteurs principaux: | , , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866914968702550016 |
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| author | Wang, Xin Zhou, Zheng Tang, Jia-Chen Hou, Xu-Yang Guo, Hao Chien, Chih-Chun |
| author_facet | Wang, Xin Zhou, Zheng Tang, Jia-Chen Hou, Xu-Yang Guo, Hao Chien, Chih-Chun |
| contents | We present a generalization of the geometric phase to pure and thermal states in $\mathcal{PT}$-symmetric quantum mechanics (PTQM) based on the approach of the interferometric geometric phase (IGP). The formalism first introduces the parallel-transport conditions of quantum states and reveals two geometric phases, $θ^1$ and $θ^2$, for pure states in PTQM according to the states under parallel-transport. Due to the non-Hermitian Hamiltonian in PTQM, $θ^1$ is complex and $θ^2$ is its real part. The imaginary part of $θ^1$ plays an important role when we generalize the IGP to thermal states in PTQM. The generalized IGP modifies the thermal distribution of a thermal state, thereby introducing effective temperatures. At certain critical points, the generalized IGP exhibits discrete jumps at finite temperatures, signaling a geometric phase transition. We demonstrate the finite-temperature geometric phase transition in PTQM by a two-level system and visualize its results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_07442 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Interferometric Geometric Phases of $\mathcal{PT}$-symmetric Quantum Mechanics Wang, Xin Zhou, Zheng Tang, Jia-Chen Hou, Xu-Yang Guo, Hao Chien, Chih-Chun Quantum Physics Mesoscale and Nanoscale Physics Other Condensed Matter We present a generalization of the geometric phase to pure and thermal states in $\mathcal{PT}$-symmetric quantum mechanics (PTQM) based on the approach of the interferometric geometric phase (IGP). The formalism first introduces the parallel-transport conditions of quantum states and reveals two geometric phases, $θ^1$ and $θ^2$, for pure states in PTQM according to the states under parallel-transport. Due to the non-Hermitian Hamiltonian in PTQM, $θ^1$ is complex and $θ^2$ is its real part. The imaginary part of $θ^1$ plays an important role when we generalize the IGP to thermal states in PTQM. The generalized IGP modifies the thermal distribution of a thermal state, thereby introducing effective temperatures. At certain critical points, the generalized IGP exhibits discrete jumps at finite temperatures, signaling a geometric phase transition. We demonstrate the finite-temperature geometric phase transition in PTQM by a two-level system and visualize its results. |
| title | Interferometric Geometric Phases of $\mathcal{PT}$-symmetric Quantum Mechanics |
| topic | Quantum Physics Mesoscale and Nanoscale Physics Other Condensed Matter |
| url | https://arxiv.org/abs/2401.07442 |