Topological Charge of Causality at a PT-Symmetric Exceptional Point
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918477004013568 |
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| author | Liu, Kejun |
| author_facet | Liu, Kejun |
| contents | Causality in linear response is conventionally treated as a binary property: a response function is either analytic in the upper half-plane or it is not. We show that in a PT-symmetric open dimer it instead carries a topological charge. As the gain-loss parameter crosses the exceptional point, a single pole of the reflection coefficient migrates into the upper half-plane, the Blaschke winding number jumps from 0 to 1, and standard Kramers-Kronig (KK) reconstruction acquires a Lorentzian residual fixed by the pole residue. The transition is sharp, protected by the codimension-one structure of the exceptional point, and directly measurable in a one-port reflection experiment. Most strikingly, the violation magnitude scales as Delta_KK ~ |gamma - gamma_c|^nu with nu ~ -1.08 in the single-port geometry: the breakdown of standard KK is strongest at threshold and weakens deeper in the broken phase. We derive the exact reflection coefficient, verify the residue-corrected dispersion relation, and propose a THz time-domain spectroscopy protocol that detects the topological charge through the residual itself. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_00117 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Topological Charge of Causality at a PT-Symmetric Exceptional Point Liu, Kejun Quantum Physics Mathematical Physics 81S22, 81Q12, 47A56 Causality in linear response is conventionally treated as a binary property: a response function is either analytic in the upper half-plane or it is not. We show that in a PT-symmetric open dimer it instead carries a topological charge. As the gain-loss parameter crosses the exceptional point, a single pole of the reflection coefficient migrates into the upper half-plane, the Blaschke winding number jumps from 0 to 1, and standard Kramers-Kronig (KK) reconstruction acquires a Lorentzian residual fixed by the pole residue. The transition is sharp, protected by the codimension-one structure of the exceptional point, and directly measurable in a one-port reflection experiment. Most strikingly, the violation magnitude scales as Delta_KK ~ |gamma - gamma_c|^nu with nu ~ -1.08 in the single-port geometry: the breakdown of standard KK is strongest at threshold and weakens deeper in the broken phase. We derive the exact reflection coefficient, verify the residue-corrected dispersion relation, and propose a THz time-domain spectroscopy protocol that detects the topological charge through the residual itself. |
| title | Topological Charge of Causality at a PT-Symmetric Exceptional Point |
| topic | Quantum Physics Mathematical Physics 81S22, 81Q12, 47A56 |
| url | https://arxiv.org/abs/2605.00117 |