{"paper":{"title":"The Child-Langmuir law in the quantum domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.plasm-ph","quant-ph"],"primary_cat":"cond-mat.mes-hall","authors_text":"Debabrata Biswas, Raghwendra Kumar","submitted_at":"2013-04-29T05:59:33Z","abstract_excerpt":"It is shown using dimensional analysis that the maximum current density J_{QCL} transported on application of a voltage V_g across a gap of size D follows the relation J_{QCL} ~ \\hbar^{3 - 2\\alpha} V_g^\\alpha /D^{5 - 2\\alpha}. The classical Child-Langmuir result is recovered at \\alpha = 3/2 on demanding that the scaling law be independent of \\hbar. For a nanogap in the deep quantum regime, additional inputs in the form of appropriate boundary conditions and the behaviour of the exchange-correlation potential show that \\alpha = 5/14. This is verified numerically for several nanogaps. It is also"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.7570","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"}