{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"da635cdda0b043b0fb0e831d3630a5a64cab58f3520ef2866ee1f6eb943b232b","created":"2026-10-03T07:17:58Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"8098ca37de09debcf26293cea17943f0dd3ce9100e4edc87219380c9c82c550d","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"identification","assisted_by":[],"external_id":"cm.chaos-scrambling.bound-saturation","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"Theory says scrambling at temperature $T$ cannot grow faster than the rate $2\\pi k_{\\mathrm{B}} T/\\hbar$, and black holes and SYK reach this limit. Whether any laboratory material or ordinary lattice model in which each site holds only a few quantum states reaches it is unknown.","posed_since":"2015","precise":"The Maldacena-Shenker-Stanford bound $\\lambda_L \\le 2\\pi k_B T/\\hbar$ holds for regularized thermal OTOCs, and large-N lattice models (SYK chains, Gu, Qi, Stanford 2017) saturate it. For a lattice model with fixed, finite local Hilbert-space dimension (no large-N or semiclassical parameter), determine whether a parametrically wide exponential-growth window exists as $T \\to 0$ and, if so, whether $\\lambda_L \\hbar/(2\\pi k_B T) \\to 1$ can be reached; or prove a bound strictly below 1. Answer: an explicit model or a bound.","problem_ref":null,"references":"","settled_by":"A controlled computation of $\\lambda_{\\mathrm{L}}(T)$ in a microscopic lattice model with finite local dimension, or direct OTOC measurement in a quantum simulator at temperatures where quantum effects dominate.","status_note":"Large-N lattice models saturate the bound; no finite-local-dimension example is known.","title":"Can a lattice with few states per site saturate the chaos bound","topic_ref":"c681d6b7c25d1a7c6ef6a216819426033bd04126d74656c004cc4a70c0ac92e1"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"3effcf478c7155a478a70f525bdf9d68613645a3c457ace60b345c39d6e152c1","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"bd8453f60ccf6dd676c5d0391469f7e4f3184e4a5e59662495bb30e092607401","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"dVaCqMCsTKEelVRzv9GUtk1-1oTFrb8FGJFMp9uFvF4VWYXqcD4X59xS1SDI7JKtDifHAg9hrXMkSlf6vjqsDQ"},"schema":"pubphys.envelope/1"},"record_hash":"3effcf478c7155a478a70f525bdf9d68613645a3c457ace60b345c39d6e152c1","leaf_index":914}