{"paper":{"title":"Anderson localization of phonons in dimension $d=1,2,3$ : finite-size properties of the Inverse Participation Ratios of eigenstates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.dis-nn","authors_text":"Cecile Monthus, Thomas Garel","submitted_at":"2010-03-31T08:01:53Z","abstract_excerpt":"We study by exact diagonalization the localization properties of phonons in mass-disordered harmonic crystals of dimension $d=1,2,3$. We focus on the behavior of the typical Inverse Participation Ratio $Y_2(\\omega,L)$ as a function of the frequency $\\omega$ and of the linear length $L$ of the disordered samples. In dimensions $d=1$ and $d=2$, we find that the low-frequency part $\\omega \\to 0$ of the spectrum satisfies the following finite-size scaling $L Y_2(\\omega,L)=F_{d=1}(L^{1/2} \\omega)$ in dimension $d=1$ and $L^2 Y_2(\\omega,L)=F_{d=2}((\\ln L)^{1/2} \\omega)$ in dimension $d=2$, with the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.5988","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"}