Marcus D. Collins | Searcharxiv

arXiv2026

Fundamental Tests of Quantum Geometric Bounds in Ionic and Covalent Insulators using Inelastic X-Ray Scattering

Quantum geometry underlies many fundamental properties of materials, but it has remained largely inaccessible to direct experiment. Here we demonstrate that inelastic x-ray scattering (IXS) provides a direct, quantitative probe of quantum geometry and quantum information in solids. Studying two prototype insulators, covalently bonded diamond and ionically bonded LiF, we measure the density response and experimentally determine the quantum Fisher information, the associated Bures metric, and the electron localization length. These measurements enable a quantitative comparison of quantum geometry for two distinct bonding environments. We find that the dimensionless quantum weight, $aK(q)$, which quantifies the longitudinal localization of quantum information, is constrained by fundamental electrostatic bounds in both materials. Crucially, the quantum weight of diamond exceeds that of LiF, indicating that covalent bonds exhibit a higher degree of delocalization and higher density of quantum information than the ionic bonds. Our results establish a direct experimental relationship between quantum information, electron localization, and chemical bonding, and identify IXS as a powerful tool for measuring quantum geometry in materials.

cond-mat.mes-hall↗

arXiv2008

Line tensions, correlation lengths, and critical exponents in lipid membranes near critical points

Membranes containing a wide variety of ternary mixtures of high chain-melting temperature lipids, low chain-melting temperature lipids, and cholesterol undergo lateral phase separartion into coexisting liquid phases at a miscibility transition. When membranes are prepared from a ternary lipid mixture at a critical composition, they pass through a miscibility critical point at the transition temperature. Since the critical temperature is typically on the order of room temperature, membranes provide an unusual opportunity in which to perform a quantitative study of biophysical systems that exhibit critical phenomena in the two-dimensional Ising universality class. As a critical point is approached from either high or low temperature, the scale of fluctuations in lipid composition, set by the correlation length, diverges. In addition, as a critical point is approached from low temperature, the line tension between coexisting phases decreases to zero. Here we quantitatively evaluate the temperature dependence of line tension between liquid domains and of fluctuation correlation lengths in lipid membranes in order to extract a critical exponent, nu. We obtain nu=1.2 plus or minus 0.2, consistent with the Ising model prediction nu=1. We also evaluate the probability distributions of pixel intensities in fluoresence images of membranes. From the temperature dependence of these distributions above the critical temperature, we extract an independent critical exponent beta=0.124 plus or minus 0.03 which is consistent with the Ising prediction of beta=1/8.

cond-mat.soft↗