{"paper":{"title":"Aging and linear response in the H\\'ebraud-Lequeux model for amorphous rheology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.soft","authors_text":"Didier Bresch (LAMA), Julien Olivier (I2M), Peter Sollich (KCL)","submitted_at":"2016-11-21T08:38:37Z","abstract_excerpt":"We analyse the aging dynamics of the H\\'ebraud-Lequeux model, a self-consistent stochastic model for the evolution of local stress in an amorphous material. We show that the model exhibits initial-condition dependent freezing: the stress diffusion constant decays with time as $D\\sim 1/t^2$ during aging so that the cumulative amount of memory that can be erased, which is given by the time integral of $D(t)$, is finite. Accordingly the shear stress relaxation function, which we determine in the long-time regime, only decays to a plateau and becomes progressively elastic as the system ages. The f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.06681","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}