{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"eac821cc04675608bbe61dadd57eee8dfcd44c2891e64a1de79aad2e169a8568","created":"2026-10-03T07:17:59Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"1b9b838e5fa24dbe3a286d8c75036d17ba2ba299fb4a3881f9efb247b7f68e6b","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"mechanism","assisted_by":[],"external_id":"cm.eth.weak-integrability-breaking","kind":"phenomenon","literature_status":"open","n":"1","parents":[],"plain":"When a solvable chain of interacting spins is perturbed slightly, it should eventually thermalize, but how long that takes and through which intermediate states is unclear. Small-system numerics often show slower relaxation than simple perturbation theory predicts.","posed_since":"","precise":"Take an integrable lattice Hamiltonian $H_0$ (e.g. the XXZ chain) plus a generic local perturbation g V. Determine the thermalization time $\\tau(g)$ of local observables and the intermediate quasi-stationary state (a deformed generalized Gibbs ensemble) in the limit $L \\to \\infty$ taken before $g \\to 0$, and explain any departure from the Fermi golden rule scaling $\\tau \\sim g^{-2}$. An answer is a controlled kinetic theory that predicts $\\tau(g)$ and the prethermal state for given $H_0$ and $V$, checked against large-scale numerics.","problem_ref":null,"references":"","settled_by":"Large-system numerics (tensor networks or quantum simulation) of $\\tau(g)$ over at least a decade in $g$, matched by a kinetic theory derived from $H_{0}$ and $V$.","status_note":"","title":"How thermalization sets in when integrability is weakly broken","topic_ref":"f62a7d7a92b8ce372b8637292294f8e379b3819f39a5ca4ca46a9a2b536b312c"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"a7060de5bf7805478da1cca6042c6f103bd2642ff9d6d3738d9b00ba74b4c273","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"f910449baa2b2707ce0b9ea69b4b31e58ae14c6f48a4d92689d75e93fe6cf9f5","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"ajha91Quy9mvk2YGUhie8m7TDVelBcpBCE1oGMrh4cHw9HIWAeHrcu842UnJuy8LkSegM_A-bLLhk7S2Jx4NCQ"},"schema":"pubphys.envelope/1"},"record_hash":"a7060de5bf7805478da1cca6042c6f103bd2642ff9d6d3738d9b00ba74b4c273","leaf_index":973}