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Encounter Propagator for Multiple Targets: A Dirichlet-to-Neumann Spectral Formalism — arXiv:2609.19995

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.19995
License (as archived): CC0-1.0
Archived: 2026-10-10T04:35:12.134Z
SHA-256 of the archived text: eb6041741dd1a38bde2074857126608742f566f86b45aa7b114b6885ead2d9c3
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How to cite

Encounter Propagator for Multiple Targets: A Dirichlet-to-Neumann Spectral Formalism — arXiv:2609.19995 — arXiv (en), https://arxiv.org/abs/2609.19995 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_a620dfdfdb80 (Metraipolis archive dc_a620dfdfdb80, sha256 eb6041741dd1a38bde2074857126608742f566f86b45aa7b114b6885ead2d9c3)

BibTeX

@misc{dca620dfdfdb80,
  title = {Encounter Propagator for Multiple Targets: A Dirichlet-to-Neumann Spectral Formalism — arXiv:2609.19995},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.19995},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_a620dfdfdb80; sha256 eb6041741dd1a38bde2074857126608742f566f86b45aa7b114b6885ead2d9c3},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.19995. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We develop an encounter-based formulation of restricted diffusion in a bounded domain with multiple targets, resolving separately the boundary local time accumulated on each target. Unlike the single-target problem, the target projection operators do not generally commute with the governing Dirichlet-to-Neumann (DtN) operator, so that its eigenbasis does not diagonalize the local-time dependence. We overcome this difficulty by decomposing the DtN operator into target-restricted blocks. Multi-dimensional Laplace inversion then yields a convergent switching expansion, whose successive terms describe alternating diffusive transfers between the targets. We also derive an equivalent operator-valued renewal equation. For two targets, diagonalizing the target-restricted blocks provides an explicit spectral representation in terms of two DtN block spectra and an inter-target coupling matrix. When the coupling preserves spectral modes, the switching series can be resummed exactly in terms of modified Bessel functions. In general, as the off-diagonal DtN block is smoothing for separated targets, one can resort to low-rank finite-dimensional approximations. We examine an effective two-mode reduction for small, well-separated targets and identify a regime in which repeated inter-target transfers are progressively suppressed. Probabilistic interpretations and implications for diffusion-controlled reactions are discussed.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-18 in math.NA).
Categorie arXiv: Statistical Mechanics (cond-mat.stat-mech) ; Mathematical Physics (math-ph); Numerical Analysis (math.NA); Spectral Theory (math.SP).
Pagina del lavoro: https://arxiv.org/abs/2609.19995 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-10T04:10:13.346Z dalla pagina https://arxiv.org/catchup/math.NA/2026-09-18?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).