{"paper":{"title":"Dynamical phase retrieval for Schr{\\\"o}dinger evolution on finite graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CO","math.MP"],"primary_cat":"math.CA","authors_text":"Azita Mayeli (CUNY), Philippe Jaming (IMB)","submitted_at":"2026-07-29T09:51:24Z","abstract_excerpt":"We study dynamical phase retrieval for Schr\\''odinger evolutions on finite connected graphs. Let \\[ H\\_Q=\\Delta\\_G+Q \\] be a graph Schr\\''odinger operator with a real diagonal potential. We investigate when phaseless data obtained from the associated Schr\\''odinger evolution \\[ |e^{-itH\\_Q}u\\_0(j)|, \\qquad 0\\leq t\\leq T,\\ j\\in V, \\] determines the initial state $u\\_0\\in\\C^V$ up to a global phase. We give a uniqueness criterion in terms of the eigenvalues and eigenvectors of $H\\_Q$. The assumptions are a $B\\_2$ condition on the spectrum, meaning that the sums $\\lambda\\_j+\\lambda\\_k$ determine t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.26705","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.26705/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}