{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"af08d90412c8af47677e17b944f13f15fbfa9cd14a4795d2b611cbb84d6d63b3","created":"2026-10-03T07:18:00Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"b0b29b860b3d8c24430885c8fdfd305e34fa601722f5d889d58b0a6b72256ba2","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":[],"external_id":"cm.lattice-transport.diffusion-constant-computability","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"In a generic chain of interacting quantum spins at high temperature, energy and spin spread diffusively at a definite rate, but no method computes this rate with a guaranteed error at reasonable cost. Exact simulation becomes exponentially expensive because the quantum state grows highly entangled.","posed_since":"","precise":"For a nonintegrable local spin chain (e.g. the mixed-field Ising chain $H=\\sum_i J Z_i Z_{i+1}+h_x X_i+h_z Z_i$) at infinite temperature, compute the energy diffusion constant $D$ from the Kubo formula to relative accuracy $\\epsilon$ at classical cost polynomial in $1/\\epsilon$, with an a posteriori error estimate. Operator-truncation methods such as dissipation-assisted operator evolution (Rakovszky, von Keyserlingk, Pollmann, arXiv:2004.05177) converge empirically but carry no general error guarantee. Answer: an algorithm with controlled error, or evidence that controlled accuracy needs cost exponential in $1/\\epsilon$.","problem_ref":null,"references":"","settled_by":"An algorithm with certified error bars reproducing D to 1 percent in a benchmark chain, cross-checked by an independent method on the same model.","status_note":"Truncation methods since 2020 give mutually consistent D estimates in benchmark chains without a general error guarantee.","title":"Controlled efficient computation of high-temperature diffusion constants","topic_ref":"4eabb15038d6d57d5e03c97f1f539dd576f4c861190c15bebd3e84acc25a5dc8"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"9ef0e5def580e389a16ccebd05435aa68294489d420db3eeaf7e1d5d386a5711","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"5306844ea9424965fc1adcab136e3f62598fed407b15ea685a762188fc4c284a","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"VBE8xluBxXXXeUC7tXq25DPByTVBg41INsykehwe3t162MhTgp5xpOJUY7585aNUcit2xq0erV9coLK_bBf9CA"},"schema":"pubphys.envelope/1"},"record_hash":"9ef0e5def580e389a16ccebd05435aa68294489d420db3eeaf7e1d5d386a5711","leaf_index":1061}