{"paper":{"title":"Localization in a rough billiard: A sigma model formulation","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat","authors_text":"Klaus M. Frahm","submitted_at":"1997-02-15T17:19:27Z","abstract_excerpt":"We consider the quantum dynamics of a particle in a weakly rough billiard. The Floquet operator for reflection at the boundary is obtained as a unitary band matrix. The resulting dynamics in angular momentum space can be treated in the framework of the one-dimensional supersymmetric nonlinear sigma model. We find analytically localization and the corresponding localization length $\\xi=D_{cl}$ where $D_{cl}$ is the classical diffusion constant due to boundary scattering."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/9702145","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"}