{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"46aaa0b43e88dbe7d3e57b72e90669ed6f0be84ed2c76c13e2238e055ae5a446","created":"2026-10-03T07:18:11Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"335a4caf6d3f6a73f4a2e5ccb328f4c94f2a337a422134786d182a2917091e47","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"stat.long-range-interactions.qss-lifetime-hmf","kind":"well-posed","literature_status":"contested","n":"1","parents":[],"plain":"In the simplest model of particles on a circle that all attract each other, the system gets stuck in non-equilibrium states for a time that grows with the number of particles N. Simulations and kinetic theory disagree on how fast it grows.","posed_since":"2004","precise":"For the Hamiltonian mean-field model $H = \\sum_i p_i^2/2 + (1/2N) \\sum_{(i,j)} [1 - \\cos(\\theta_i - \\theta_j)]$ started in a spatially homogeneous, Vlasov-stable quasi-stationary state, determine the exponent $\\delta$ in the relaxation time $\\tau \\sim N^{\\delta}$. Simulations report $\\delta$ approximately 1.7, while kinetic theory (the Lenard-Balescu collision term vanishes for 1D homogeneous systems, leaving $1/N^2$ terms) predicts $\\delta = 2$. An answer is $\\delta$ and its dependence on the initial distribution and energy.","problem_ref":null,"references":"","settled_by":"Simulations at N large enough to separate N^1.7 from $N^2$ scaling, together with a kinetic theory that reproduces the measured prefactor.","status_note":"","title":"Lifetime of quasi-stationary states in the Hamiltonian mean-field model","topic_ref":"ab4bc09e1403451f008cb53272599f798703ab0cadd239986a649c7b5254b41d"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"adf5a5622bfa793a612b8970fcbd748e076c4c71e8aefa540ee89a0e029e0b51","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"2de47d323ee5f15705cddb5d79c25fa2f9d6a67c551789da2e81df070e17d45e","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"w9-l5-_MC7IdN05oeTNT_vKgfPc-b0OR-JhI7pIZ20icHEvmaL_nbDvkBAc8-XiV8gBo_ATp3za_IQV5uSp6DQ"},"schema":"pubphys.envelope/1"},"record_hash":"adf5a5622bfa793a612b8970fcbd748e076c4c71e8aefa540ee89a0e029e0b51","leaf_index":2097}