{"paper":{"title":"Trace asymptotics formula for the Schr\\\"odinger operators with constant magnetic fields","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Anh Tuan Duong, Mouez Dimassi","submitted_at":"2013-02-17T14:49:30Z","abstract_excerpt":"In this paper, we consider the 2D- Schr\\\"odinger operator with constant magnetic field $H(V)=(D_x-By)^2+D_y^2+V_h(x,y)$, where $V$ tends to zero at infinity and $h$ is a small positive parameter. We will be concerned with two cases: the semi-classical limit regime $V_h(x,y)=V(h x,h y)$, and the large coupling constant limit case $V_h(x,y)=h^{-\\delta} V(x,y)$. We obtain a complete asymptotic expansion in powers of $h^2$ of ${\\rm tr}(\\Phi(H(V),h))$, where $\\Phi(\\cdot,h)\\in C^\\infty_0(\\mathbb R;\\mathbb R)$. We also give a Weyl type asymptotics formula with optimal remainder estimate of the counti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.4074","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"}