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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2512.20253 |
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| _version_ | 1866914217237413888 |
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| author | Saurabh, Prasoon |
| author_facet | Saurabh, Prasoon |
| contents | Standard topological invariants, such as the Chern number and Berry phase, form the bedrock of modern quantum matter classification. However, we demonstrate that this framework undergoes a \textbf{catastrophic failure} in the presence of essential singularities -- ubiquitous in open, driven, and non-Hermitian systems ("Wild" regime). In these settings, the local geometric tensor diverges, rendering standard invariants ill-defined and causing perturbative predictions to deviate from reality by order unity ($\sim 100\%$). We resolve this crisis by introducing the \textbf{Floquet-Monodromy Spectroscopy (FMS)} protocol, a pulse-level control sequence, which experimentally extracts the hidden \textit{Stokes Phenomenon} -- the "missing" geometric data that completes the topological description. By mapping the singularity's Stokes multipliers to time-domain observables, FMS provides a rigorous experimental bridge to \textbf{Resurgence Theory}, allowing for the exact reconstruction of non-perturbative physics from divergent asymptotic series. We validate this framework on a superconducting qudit model, demonstrating that the "Stokes Invariant" serves as the next-generation quantum number for classifying phases of matter beyond the reach of conventional topology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_20253 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum Geometric Tensor in the Wild: Resolving Stokes Phenomena via Floquet-Monodromy Spectroscopy Saurabh, Prasoon Quantum Physics Mesoscale and Nanoscale Physics Mathematical Physics 81Q93, 34M40, 32C38 J.2; G.1.7; F.2.1 Standard topological invariants, such as the Chern number and Berry phase, form the bedrock of modern quantum matter classification. However, we demonstrate that this framework undergoes a \textbf{catastrophic failure} in the presence of essential singularities -- ubiquitous in open, driven, and non-Hermitian systems ("Wild" regime). In these settings, the local geometric tensor diverges, rendering standard invariants ill-defined and causing perturbative predictions to deviate from reality by order unity ($\sim 100\%$). We resolve this crisis by introducing the \textbf{Floquet-Monodromy Spectroscopy (FMS)} protocol, a pulse-level control sequence, which experimentally extracts the hidden \textit{Stokes Phenomenon} -- the "missing" geometric data that completes the topological description. By mapping the singularity's Stokes multipliers to time-domain observables, FMS provides a rigorous experimental bridge to \textbf{Resurgence Theory}, allowing for the exact reconstruction of non-perturbative physics from divergent asymptotic series. We validate this framework on a superconducting qudit model, demonstrating that the "Stokes Invariant" serves as the next-generation quantum number for classifying phases of matter beyond the reach of conventional topology. |
| title | Quantum Geometric Tensor in the Wild: Resolving Stokes Phenomena via Floquet-Monodromy Spectroscopy |
| topic | Quantum Physics Mesoscale and Nanoscale Physics Mathematical Physics 81Q93, 34M40, 32C38 J.2; G.1.7; F.2.1 |
| url | https://arxiv.org/abs/2512.20253 |