Interaction-Induced Structural Redistribution and the Emergence of Particle-Like Localization
Year: 2026
Type: preprint
Abstract: We develop a structural framework in which particle-like localization emerges from interaction-induced redistribution of probability across an ordered hierarchy of microscopic sectors. The frame-work begins with a normalized sector distribution whose weights characterize the degree to whichmicroscopic structure is associated with each sector. Neighboring sectors are coupled locally, andtheir weight differences contribute to a structural functional that determines the cost of reorganizingthe distribution. Interaction therefore does not act as an independent collapse postulate. Instead,its strength controls the extent to which the structural hierarchy can be explored and the degree towhich sector weights are redistributed.We show that finite interactions generically allow partial structural reorganization rather thanautomatic single-sector selection. As the available interaction energy increases, additional structuraltransitions become accessible and the sector distribution can become progressively concentrated. Inthe strong-interaction limit, subject to the stability conditions of the structural flow, the distributionmay approach a single dominant sector. We quantify this process using the sector concentrationand the effective number of occupied sectors.The resulting concentration has a direct representation in the density-operator formalism. For asector decomposition ρ =∑︁ i piPi, structural concentration implies Tr(ρ2) → 1. When the limitingsector is rank one, the state consequently approaches a pure-state representation ρ = |ψ⟩⟨ψ|, withsector probabilities taking the standard form pi = |⟨Si|ψ⟩|2. A minimal ordered four-sector toymodel explicitly demonstrates the continuous redistribution, threshold accessibility, and strong-interaction concentration predicted by the framework. We finally identify interaction-dependentconcentration and purity as experimentally testable signatures of the proposed mechanism
Author: Kim, HyeongWoo
Institution: Hanyang University
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204847285