{"schema":"pubphys.bundle/1","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 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