{"paper":{"title":"Modulational instabilities in lattices with power-law hoppings and interactions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"nlin.PS","authors_text":"Andrea Trombettoni, Giacomo Gori, Tommaso Macri","submitted_at":"2012-12-03T19:20:40Z","abstract_excerpt":"We study the occurrence of modulational instabilities in lattices with non-local, power-law hoppings and interactions. Choosing as a case study the discrete nonlinear Schr\\\"odinger equation, we consider one-dimensional chains with power-law decaying interactions (with exponent \\alpha) and hoppings (with exponent \\beta): An extensive energy is obtained for \\alpha, \\beta>1. We show that the effect of power-law interactions is that of shifting the onset of the modulational instabilities region for \\alpha>1. At a critical value of the interaction strength, the modulational stable region shrinks to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.0495","kind":"arxiv","version":2},"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"}