{"paper":{"title":"Operator Dynamics in Brownian Quantum Circuit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","hep-th"],"primary_cat":"cond-mat.str-el","authors_text":"Tianci Zhou, Xiao Chen","submitted_at":"2018-05-23T17:46:29Z","abstract_excerpt":"We explore the operator dynamics in a random $N$-spin model with pairwise interactions (Brownian quanum circuit). We introduce the height $h$ of an operator to characterize its spatial extent, and derive the master equation of the height probability distribution. The study of an initial simple operator with $h = 1$ (minimal nonzero height) shows that the mean height, which is proportional to the squared commutator, has an initial exponential growth. It then slows down around the scrambling time $\\sim\\log N$ and finally saturates to a steady state in a manner similar to the logistic function. T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.09307","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"}