Year: 2026
Type: preprint
Abstract: Spatial discreteness generically supplies preferred microscopic directions, whereas a relativistic long-wave sector requires an isotropic propagation cone. We examine this tension in a classical kinematical model of mobile Voronoi cells carrying compact internal phases. Linearization about a uniform phase vacuum gives a face-area-weighted graph wave equation. For each periodic realization, a discrete corrector problem determines the quadratic coefficient of the lowest Bloch branch. We prove the following conditional statement: if the stationary ergodic marked-cell ensemble admits a deterministic, finite, positive-definite homogenized tensor, rotational invariance of its law forces that tensor to equal c0 I. The two-derivative phase action then has one isotropic limiting speed. In 88 independent Poisson-Voronoi realizations with 8 <= N <= 216, the mean relative eigenvalue spread decreases from 0.2159 (95% bootstrap interval [0.1829, 0.2524]) to 0.0391 ([0.0324, 0.0454]). Direct Metropolis sampling of two finite-modulus measures gives anisotropies 0.1110 and 0.1063, consistent with independent importance-reweighted estimates (|z| < 0.23). Direct Bloch diagonalization also recovers the corrector coefficients as k l -> 0, while finite-cell corrections enter at fourth derivative order. These results establish a controlled route to Lorentz-like propagation in the two-derivative phase sector; they do not establish microscopic boost invariance or a universal cone for geometric modes.
Source: Research Square
Author: Shengliang Dong
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204565629