{"paper":{"title":"Statistical diagonalization of a random biased Hamiltonian: the case of the eigenvectors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mes-hall","cond-mat.stat-mech"],"primary_cat":"quant-ph","authors_text":"Gr\\'egoire Ithier, Saeed Ascroft","submitted_at":"2018-03-21T20:41:06Z","abstract_excerpt":"We present a non perturbative calculation technique providing the mixed moments of the overlaps between the eigenvectors of two large quantum Hamiltonians: $\\hat{H}_0$ and $\\hat{H}_0+\\hat{W}$, where $\\hat{H}_0$ is deterministic and $\\hat{W}$ is random. We apply this method to recover the second order moments or Local Density Of States in the case of an arbitrary fixed $\\hat{H}_0$ and a Gaussian $\\hat{W}$. Then we calculate the fourth order moments of the overlaps in the same setting. Such quantities are crucial for understanding the local dynamics of a large composite quantum system. In this c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.08122","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"}