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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2512.21662 |
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| _version_ | 1866918263840047104 |
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| author | Saurabh, Prasoon |
| author_facet | Saurabh, Prasoon |
| contents | Standard spectroscopic protocols model the dynamics of open quantum systems as a superposition of isolated, exponentially decaying eigenmodes. This paradigm fails fundamentally at Exceptional Points, where the eigenbasis collapses and the response becomes dominated by non-diagonalizable Jordan blocks. We resolve this ambiguity by introducing a geometric framework based on \textit{Dissipative Mixed Hodge Modules} (DMHM). By replacing the scalar linewidth with a topological \textit{Weight Filtration}, we derive ``Weight Filtered Spectroscopy'' (WFS)--a protocol that spatially separates decay channels based on the nilpotency rank of the Liouvillian. We demonstrate that WFS acts as a dissipative x-ray, quantifying dissipative leakage in molecular polaritons and certifying topological isolation in Non-Hermitian Aharonov-Bohm rings. This establishes that topological protection persists as an algebraic invariant even when the spectral gap is closed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_21662 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spectroscopic Search for Topological Protection in Open Quantum Hardware: The Dissipative Mixed Hodge Module Approach Saurabh, Prasoon Quantum Physics Mesoscale and Nanoscale Physics Mathematical Physics Chemical Physics 81S22, 81Q12, 32S35, 14F10 J.2; E.4; B.8.1 Standard spectroscopic protocols model the dynamics of open quantum systems as a superposition of isolated, exponentially decaying eigenmodes. This paradigm fails fundamentally at Exceptional Points, where the eigenbasis collapses and the response becomes dominated by non-diagonalizable Jordan blocks. We resolve this ambiguity by introducing a geometric framework based on \textit{Dissipative Mixed Hodge Modules} (DMHM). By replacing the scalar linewidth with a topological \textit{Weight Filtration}, we derive ``Weight Filtered Spectroscopy'' (WFS)--a protocol that spatially separates decay channels based on the nilpotency rank of the Liouvillian. We demonstrate that WFS acts as a dissipative x-ray, quantifying dissipative leakage in molecular polaritons and certifying topological isolation in Non-Hermitian Aharonov-Bohm rings. This establishes that topological protection persists as an algebraic invariant even when the spectral gap is closed. |
| title | Spectroscopic Search for Topological Protection in Open Quantum Hardware: The Dissipative Mixed Hodge Module Approach |
| topic | Quantum Physics Mesoscale and Nanoscale Physics Mathematical Physics Chemical Physics 81S22, 81Q12, 32S35, 14F10 J.2; E.4; B.8.1 |
| url | https://arxiv.org/abs/2512.21662 |