{"paper":{"title":"The spectral dimension controls the decay of the quantum first detection probability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"David A. Kessler, Eli Barkai, Felix Thiel","submitted_at":"2018-02-15T12:27:40Z","abstract_excerpt":"We consider a quantum system that is initially localized at $x_{in}$ and that is repeatedly projectively probed with a fixed period $\\tau$ at position $x_d$. We ask for the probability that the system is detected in $x_d$ for the very first time, $F_n$, where $n$ is the number of detection attempts. We relate the asymptotic decay and oscillations of $F_n$ with the system's energy spectrum, which is assumed to be absolutely continuous. In particular $F_n$ is determined by the Hamiltonian's measurement spectral density of states (MSDOS) $f(E)$ that is closely related to the density of energy sta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.05504","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"}