Homometric Elastic Lattices and Laminates: Identical Bulk Dispersion and Robust Thermal Separation
Year: 2026
Type: article
Abstract: Periodic diffraction and complete vector Bloch dispersion can agree for two stable elastic specimens whose contacted thermal conductances differ. This paper constructs homometric density laminates with a positive conductance gap after including all three polarizations, every propagating angle, and the full frequency integral. Exact transfer identities, contact factorization, spectral products, and grazing-incidence estimates expose information that the two bulk measurements do not determine. An objective finite-range interaction realizes the construction in a positive-mass harmonic lattice. For one cell, explicit temperature intervals and conductance margins hold uniformly over every integer refinement and within a shared parameter box. The complete lattice conductance converges to its continuum value on compact positive-temperature intervals. Mass compensation, termination classification, calibrated contact identification, passive loss, thermal re-emission, and optimal reservoir redistribution have separate analytical certificates. A general tensor-roughness theorem controls bounded measurable elastic coefficients with uniformly positive strain energy. Local spectral traces, Hilbert-valued higher integrability, and thermal subordination give a conductance modulus independent of transverse area and refinement of the specified lattice. Finite interface displacements enter through swept volume, without slope restrictions. Cell averaging preserves the uncertainty budgets. A combined certificate permits simultaneous mass and tensor errors relative to the nominal construction. The leads remain fixed; the general constants have not been calibrated into experimentally useful fabrication tolerances. A positive Keating bond-and-angle model realizes the required relaxed continuum tensor and has no nontranslational harmonic zero modes. Chemical candidates admit an exact acoustic screening criterion: the required cubic tensor has equal longitudinal and transverse acoustic speeds along the body diagonal. A quantitative orientation-independent obstruction excludes several measured or predicted hosts from exact matching. Samarium alloys with measured negative cross moduli provide screening candidates, but no chemical pair or temperature-uniform material certificate is established. For the original nonlinear interaction in a fixed clamped cylinder, classical and quantum Gibbs states converge under mechanical scaling; even configuration observables have a controlled inverse-scale correction. An exact folded configuration explains why the coercivity comparison need not remain uniform as the reservoirs lengthen. A nonnegative objective determinant penalty excludes improper local rotations while preserving the harmonic and cubic terms. For the planar dense-lead lattice, an explicit mass-ratio condition makes every above-band localized mode kinematically accessible to two propagating phonons. A finite family of positive objective cubic controls goes further: it preserves the harmonic Hessians of both actual motifs and generically gives finite positive channel contributions at almost every transverse momentum. The algebraic strain-visibility count is sharp. These results do not establish uniform decay, convergence of the full channel integral, or nonlinear stationary transport. The unmodified cubic law and the stationary paired-response estimates retain their stated qualifications. Exact intrinsic anharmonic conductance, chemical identification, useful operating contrasts, full Keating thermal homogenization, and noisy or broadband contact recovery remain open. Further questions concern quantitative continuum-approximation thresholds, explicit endpoints for arbitrary cell counts and dense leads, and geometric or discretization classes beyond the stated positive coefficient model. The project includes editable LaTeX sources, eighteen reproducible figures, verification code, and a separate corrections report.
Author: Fathi, Kevin
Language: English
Subfield: Materials Chemistry
Field: Materials Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225598695