dorsal/arxiv
View SchemaComminution as a Non-Hermitian Quantum Field Theory: Log-Size Jump Generators, Branching Embeddings, and the Airy Solvable Sector
| Authors | Juan J. Segura |
|---|---|
| Categories | |
| ArXiv ID | 2601.06635vv1 |
| URL | https://arxiv.org/abs/2601.06635 |
| License | http://creativecommons.org/licenses/by/4.0/ |
Abstract
Pure-breakage population balance equations (PBEs) give the standard deterministic description of fragmentation and comminution. They predict mean particle size distributions, but they do not determine fluctuations, size-size correlations, or universality under coarse-graining. We develop a field-theoretic framework anchored in the PBE kernel inputs (selection rate and daughter distribution) and compatible with the stochastic Doi-Peliti approach. From homogeneous kernels we derive an exact Markov jump generator in log-size for a mass-weighted (tagged-mass) distribution, with a jump law that is a probability density fixed by the daughter distribution. The generator is generically non-self-adjoint, admits a Lindblad embedding, and has a second-quantized extension. The deterministic PBE appears as the one-body sector, while multi-point correlators encode finite-population fluctuations. We also give a binary-fragmentation embedding whose mean-field limit reproduces the PBE but whose higher correlators capture multiplicative cascade noise. For a linear Airy-type kernel, long-wavelength coarse-graining yields an effective Airy operator as a solvable quadratic sector about a stationary profile, producing explicit mode-sum formulas for equal-time connected two-point correlations. Overall, the framework separates what is fixed by kernel data from what requires additional stochastic modeling and links comminution kernels to universality classes.
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"abstract": "Pure-breakage population balance equations (PBEs) give the standard deterministic description of fragmentation and comminution. They predict mean particle size distributions, but they do not determine fluctuations, size-size correlations, or universality under coarse-graining. We develop a field-theoretic framework anchored in the PBE kernel inputs (selection rate and daughter distribution) and compatible with the stochastic Doi-Peliti approach.\n From homogeneous kernels we derive an exact Markov jump generator in log-size for a mass-weighted (tagged-mass) distribution, with a jump law that is a probability density fixed by the daughter distribution. The generator is generically non-self-adjoint, admits a Lindblad embedding, and has a second-quantized extension. The deterministic PBE appears as the one-body sector, while multi-point correlators encode finite-population fluctuations. We also give a binary-fragmentation embedding whose mean-field limit reproduces the PBE but whose higher correlators capture multiplicative cascade noise. For a linear Airy-type kernel, long-wavelength coarse-graining yields an effective Airy operator as a solvable quadratic sector about a stationary profile, producing explicit mode-sum formulas for equal-time connected two-point correlations. Overall, the framework separates what is fixed by kernel data from what requires additional stochastic modeling and links comminution kernels to universality classes.",
"arxiv_id": "2601.06635",
"authors": [
"Juan J. Segura"
],
"categories": [
"math-ph",
"cond-mat.stat-mech",
"math.MP"
],
"license": "http://creativecommons.org/licenses/by/4.0/",
"title": "Comminution as a Non-Hermitian Quantum Field Theory: Log-Size Jump Generators, Branching Embeddings, and the Airy Solvable Sector",
"url": "https://arxiv.org/abs/2601.06635",
"version": "v1"
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