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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.05335 |
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| _version_ | 1866910204532097024 |
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| author | Wang, Ming-Zhang Hou, Xu-Yang Guo, Hao |
| author_facet | Wang, Ming-Zhang Hou, Xu-Yang Guo, Hao |
| contents | Quasi-Hermitian quantum systems, including $\mathcal{PT}$-symmetric ones, can be mapped to equivalent Hermitian systems via a similarity transformation that redefines the inner product with a positive-definite metric operator. Although an instantaneous algebraic Hermitianization can be obtained locally from a positive metric operator, a stronger requirement is needed for dynamical equivalence: the similarity transformation must be proper, globally single-valued, and compatible with the modified quasi-Hermitian Schrodinger equation. We identify two distinct obstructions: geometric obstructions arising from the curvature of a metric-induced connection, and topological obstructions originating from non-trivial holonomies around non-contractible loops in parameter space. We derive explicit criteria for these obstructions and illustrate them with concrete examples. Our results establish a geometric and topological foundation for the Hermitianization of quasi-Hermitian systems, clarifying when they can be globally reduced to Hermitian ones and when intrinsic non-Hermitian features persist. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_05335 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Geometric and Topological Obstructions to Hermitianization in Quasi-Hermitian Quantum Systems Wang, Ming-Zhang Hou, Xu-Yang Guo, Hao Quantum Physics Quasi-Hermitian quantum systems, including $\mathcal{PT}$-symmetric ones, can be mapped to equivalent Hermitian systems via a similarity transformation that redefines the inner product with a positive-definite metric operator. Although an instantaneous algebraic Hermitianization can be obtained locally from a positive metric operator, a stronger requirement is needed for dynamical equivalence: the similarity transformation must be proper, globally single-valued, and compatible with the modified quasi-Hermitian Schrodinger equation. We identify two distinct obstructions: geometric obstructions arising from the curvature of a metric-induced connection, and topological obstructions originating from non-trivial holonomies around non-contractible loops in parameter space. We derive explicit criteria for these obstructions and illustrate them with concrete examples. Our results establish a geometric and topological foundation for the Hermitianization of quasi-Hermitian systems, clarifying when they can be globally reduced to Hermitian ones and when intrinsic non-Hermitian features persist. |
| title | Geometric and Topological Obstructions to Hermitianization in Quasi-Hermitian Quantum Systems |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2605.05335 |