{"paper":{"title":"Lamb Shift of Landau Levels in Two-Dimensional Electron Systems in a Multimode Resonator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Many resonator modes greatly enhance the softening of cyclotron frequency in two-dimensional electron systems","cross_cats":[],"primary_cat":"cond-mat.mes-hall","authors_text":"Aleksandr Shabanov, Dmitry Svintsov, Georgy Alymov","submitted_at":"2026-05-13T11:11:05Z","abstract_excerpt":"The use of resonators to modify the behavior of electromagnetic systems demonstrates its potential for application in a wide range of problems. However, existing theoretical studies often resort to the single-mode approximation, rarely considering a second resonator mode. In this paper, we show that including a large number of resonator modes in the model significantly enhances the softening effect of the cyclotron frequency of a two-dimensional electron system. We address this problem by demonstrating the possibility of reducing the system to a set of coupled harmonic oscillators and finding "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"including a large number of resonator modes in the model significantly enhances the softening effect of the cyclotron frequency of a two-dimensional electron system","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The interacting system can be reduced to a set of coupled harmonic oscillators whose eigenfrequencies capture the full multimode Lamb shift without significant higher-order corrections.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Accounting for many resonator modes significantly enhances the Lamb-shift softening of cyclotron frequency in 2D electron systems by mapping the problem to coupled harmonic oscillators.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Many resonator modes greatly enhance the softening of cyclotron frequency in two-dimensional electron systems","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"10e07abad514944fdf7851d99711267f7844974ebafa7738955bbc4a223197b5"},"source":{"id":"2605.13351","kind":"arxiv","version":1},"verdict":{"id":"083d8b6d-6a39-4f1f-baa4-2b0ef44ea412","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T18:27:48.448034Z","strongest_claim":"including a large number of resonator modes in the model significantly enhances the softening effect of the cyclotron frequency of a two-dimensional electron system","one_line_summary":"Accounting for many resonator modes significantly enhances the Lamb-shift softening of cyclotron frequency in 2D electron systems by mapping the problem to coupled harmonic oscillators.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The interacting system can be reduced to a set of coupled harmonic oscillators whose eigenfrequencies capture the full multimode Lamb shift without significant higher-order corrections.","pith_extraction_headline":"Many resonator modes greatly enhance the softening of cyclotron frequency in two-dimensional electron systems"},"references":{"count":30,"sample":[{"doi":"","year":1992,"title":"Quantum hall effect","work_id":"77300529-818e-4b6e-9525-6949b2445690","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2025,"title":"optical pumping of electronic quantum hall states with vortex light","work_id":"7e661d76-420b-4e49-9f71-599ded38524e","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2022,"title":"breakdown of topological protection by cav- ity vacuum fields in the integer quantum hall effect","work_id":"0f49ae4e-9b31-49a9-a5d4-a603aebb1e30","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2025,"title":"tunable vacuum-field control of fractional and integer quantum hall phases","work_id":"5cf8c3fa-5884-42e5-8b73-d77f89e4f5cb","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2024,"title":"cavity-enhanced superconductivity in mgb2 from first-principles quantum electrodynamics (qedft)","work_id":"26cd1608-a371-4dcf-b288-a82197275ac4","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":30,"snapshot_sha256":"9cffe45d81921386284ec2eea0a7bee44dd7e771188d91acaa351ebf88f28fb4","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"}