2025/12/15 by Corentin C. L. Laudicina, Laudicina, Corentin C. L., Liesbeth M. C. Janssen +3
Materials Science · Physics and Astronomy · #Material Dynamics and Properties #Theoretical and Computational Physics #Quantum Electrodynamics and Casimir Effect
paper · pdf · doi:10.48550/arxiv.2512.13092
We develop a systematic extension of mode-coupling theory (MCT) that incorporates critical dynamical fluctuations. Starting from a microscopic diagrammatic theory, we identify dominant classes of divergent diagrams near the mode-coupling transition and show that the corresponding asymptotic series dominates the mean-field below an upper critical dimension dc=8. To resum these divergences, we construct a mapping to a stochastic dynamical process in which the order parameter evolves under random spatiotemporal fields. This reformulation provides a controlled, fully dynamical derivation of an effective theory for the β-relaxation which remarkably coincides with stochastic beta-relaxation theory [T. Rizzo, EPL 106, 56003 (2014)]. All coupling constants of the latter theory are expressed microscopically in terms of the liquid static structure factor and are computed for the paradigmatic hard-sphere system. The analysis demonstrates that fluctuations alone restore ergodicity and replace the putative mean-field transition by a smooth crossover. Our results establish a predictive framework for structural relaxation beyond mean-field.