{"paper":{"title":"Fractal and chaotic solutions of the discrete nonlinear Schr\\\"odinger equation in classical and quantum systems","license":"","headline":"","cross_cats":["math.MP","nlin.CD"],"primary_cat":"math-ph","authors_text":"Fjodor V. Kusmartsev, Harj S. Dhillon, Karl E. K\\\"urten","submitted_at":"2001-01-01T00:00:00Z","abstract_excerpt":"We discuss stationary solutions of the discrete nonlinear Schr\\\"odinger equation (DNSE) with a potential of the $\\phi^{4}$ type which is generically applicable to several quantum spin, electron and classical lattice systems. We show that there may arise chaotic spatial structures in the form of incommensurate or irregular quantum states. As a first (typical) example we consider a single electron which is strongly coupled with phonons on a $1D$ chain of atoms --- the (Rashba)--Holstein polaron model. In the adiabatic approximation this system is conventionally described by the DNSE. Another rel"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0101038","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"}