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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2601.20313 |
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| _version_ | 1866914426266845184 |
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| author | Bao, Yiwei Addazi, Andrea Zha, Shuai |
| author_facet | Bao, Yiwei Addazi, Andrea Zha, Shuai |
| contents | We develop an exact framework for neutrino decoherence in power-law correlated turbulent matter, as encountered in core-collapse supernovae. Employing the Nakajima--Zwanzig projection technique, we derive an exact non-Markovian master equation for the neutrino density matrix. For kernels \( K(t) \propto t^{-ν} \), the spectral index \(ν\) characterizes the correlation structure: smaller (including negative) values of \(ν\) correspond to stronger long-range correlations. To treat ultraviolet singularities for \( ν\geq 1 \) without spoiling the fractional structure, we use a renormalization prescription based on Hadamard finite parts and analytic continuation. The exact Laplace-space solution for the survival probability is obtained. In the high-density matter basis relevant to supernovae, the solution is expressed through Mittag-Leffler functions, establishing a direct link to anomalous diffusion phenomena. For negative spectral indices (\( ν< 0 \)), the memory integral corresponds to a higher-order fractional operator. Our work clarifies how spectral index, renormalization scale, and decoherence efficiency interrelate, providing a complete analytical description and practical tools for supernova neutrino simulations. The fractional calculus formulation reveals fundamental mathematical connections between neutrino flavor evolution and other systems governed by long-range temporal correlations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_20313 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Mathematical Anatomy of Neutrino Decoherence in Red Turbulence: A Fractional Calculus Approach Bao, Yiwei Addazi, Andrea Zha, Shuai High Energy Astrophysical Phenomena We develop an exact framework for neutrino decoherence in power-law correlated turbulent matter, as encountered in core-collapse supernovae. Employing the Nakajima--Zwanzig projection technique, we derive an exact non-Markovian master equation for the neutrino density matrix. For kernels \( K(t) \propto t^{-ν} \), the spectral index \(ν\) characterizes the correlation structure: smaller (including negative) values of \(ν\) correspond to stronger long-range correlations. To treat ultraviolet singularities for \( ν\geq 1 \) without spoiling the fractional structure, we use a renormalization prescription based on Hadamard finite parts and analytic continuation. The exact Laplace-space solution for the survival probability is obtained. In the high-density matter basis relevant to supernovae, the solution is expressed through Mittag-Leffler functions, establishing a direct link to anomalous diffusion phenomena. For negative spectral indices (\( ν< 0 \)), the memory integral corresponds to a higher-order fractional operator. Our work clarifies how spectral index, renormalization scale, and decoherence efficiency interrelate, providing a complete analytical description and practical tools for supernova neutrino simulations. The fractional calculus formulation reveals fundamental mathematical connections between neutrino flavor evolution and other systems governed by long-range temporal correlations. |
| title | Mathematical Anatomy of Neutrino Decoherence in Red Turbulence: A Fractional Calculus Approach |
| topic | High Energy Astrophysical Phenomena |
| url | https://arxiv.org/abs/2601.20313 |