{"paper":{"title":"Two Coupled Harmonic Oscillators on Non-commutative Plane","license":"","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Ahmed Jellal, El Hassan El Kinani, Michael Schreiber","submitted_at":"2003-09-10T15:49:25Z","abstract_excerpt":"We investigate a system of two coupled harmonic oscillators on the non-commutative plane \\RR^2_{\\theta} by requiring that the spatial coordinates do not commute. We show that the system can be diagonalized by a suitable transformation, i.e. a rotation with a mixing angle \\alpha. The obtained eigenstates as well as the eigenvalues depend on the non-commutativity parameter \\theta. Focusing on the ground state wave function before the transformation, we calculate the density matrix \\rho_0(\\theta) and find that its traces {\\rm Tr}(\\rho_{0}(\\theta)) and {\\rm Tr}(\\rho_0^2(\\theta)) are not affected b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0309105","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"}