dorsal/arxiv
View SchemaA Lindblad and Non-Hermitian Spectral Framework for Fragmentation Dynamics and Particle Size Distributions
| Authors | Juan J. Segura |
|---|---|
| Categories | |
| ArXiv ID | 2601.06638vv1 |
| URL | https://arxiv.org/abs/2601.06638 |
| License | http://creativecommons.org/licenses/by/4.0/ |
Abstract
Population balance equations (PBEs) for pure fragmentation describe how particle size distributions (PSDs) evolve under breakage and fragment redistribution. We map a self-similar fragmentation class to: a conservative pure-jump master equation in log-size space; an exact Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) dilation whose diagonal sector reproduces that master equation; and a controlled small-jump limit where the dynamics reduce to a Fokker-Planck operator that can be symmetrized into a Schrodinger-type spectral problem. Two points ensure correctness and applicability. First, the Lindblad embedding is exact when the daughter kernel is interpreted in mass-weighted form (equivalently, when z*kappa(z) is a probability measure). Second, for genuinely non-Hermitian dynamics the stationary PSD is naturally a biorthogonal product of left and right ground states, not a naive modulus square; the usual modulus squared of psi appears only in pseudo-Hermitian or effectively dephased regimes. We then give a spectral dictionary linking typical PSD shapes to low-dimensional potential families in log-size space and outline inverse routes to infer effective potentials from data: parametric fitting with time-resolved PSDs, a direct steady-state inversion from a smoothed PSD, and an outlook toward inverse spectral ideas. A synthetic example demonstrates forward simulation and inverse parameter recovery in an Airy-type half-line model.
{
"annotation_id": "e4124b9e-d977-4958-a46c-916261bcc637",
"date_created": "2026-02-17T05:53:08.609000Z",
"date_modified": "2026-02-17T05:53:08.609000Z",
"file_hash": "7bcce9e82bbef66598075633f71457d509e73846bf1e47313087f55f0dc3504e",
"private": false,
"record": {
"abstract": "Population balance equations (PBEs) for pure fragmentation describe how particle size distributions (PSDs) evolve under breakage and fragment redistribution. We map a self-similar fragmentation class to: a conservative pure-jump master equation in log-size space; an exact Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) dilation whose diagonal sector reproduces that master equation; and a controlled small-jump limit where the dynamics reduce to a Fokker-Planck operator that can be symmetrized into a Schrodinger-type spectral problem.\n Two points ensure correctness and applicability. First, the Lindblad embedding is exact when the daughter kernel is interpreted in mass-weighted form (equivalently, when z*kappa(z) is a probability measure). Second, for genuinely non-Hermitian dynamics the stationary PSD is naturally a biorthogonal product of left and right ground states, not a naive modulus square; the usual modulus squared of psi appears only in pseudo-Hermitian or effectively dephased regimes.\n We then give a spectral dictionary linking typical PSD shapes to low-dimensional potential families in log-size space and outline inverse routes to infer effective potentials from data: parametric fitting with time-resolved PSDs, a direct steady-state inversion from a smoothed PSD, and an outlook toward inverse spectral ideas. A synthetic example demonstrates forward simulation and inverse parameter recovery in an Airy-type half-line model.",
"arxiv_id": "2601.06638",
"authors": [
"Juan J. Segura"
],
"categories": [
"cond-mat.stat-mech",
"math-ph",
"math.MP"
],
"license": "http://creativecommons.org/licenses/by/4.0/",
"title": "A Lindblad and Non-Hermitian Spectral Framework for Fragmentation Dynamics and Particle Size Distributions",
"url": "https://arxiv.org/abs/2601.06638",
"version": "v1"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "ad6db2d6-fd10-4fbd-af6f-13b4fd93dbf8",
"id": "arXiv Dataset",
"type": "Model",
"variant": "snapshot-2026-01-17",
"version": "0.1.0"
},
"user_id": 1000002
}