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Accepted · first revision · record

Title: Universal exponent of anomalous heat conduction in one dimension
Plain: In one-dimensional chains that conserve momentum, heat conductivity grows with chain length instead of staying fixed. Theory predicts universal growth exponents, but simulations of different chains disagree.
Precise: For 1D anharmonic chains conserving energy, momentum and stretch (e.g., FPUT with asymmetric or symmetric potentials), determine the exponent delta in the conductivity $\kappa(L) \sim L^\delta$. Nonlinear fluctuating hydrodynamics predicts $\delta = 1/3$ for generic asymmetric potentials (FPUT-alpha-beta: KPZ sound modes and a Levy 5/3 heat mode); for the symmetric FPUT-beta chain numerics and mode-coupling theory support $\delta = 2/5$. An answer is the exponent for each class, confirmed at sizes where finite-size drift is controlled.
Settled by: Nonequilibrium and equilibrium simulations at sizes where effective exponents stop drifting, agreeing with the hydrodynamic prediction for each class.
Kind: well-posed
Answer type: value
References: (empty)
Literature status: contested
Status note: Simulated exponents range roughly from 0.25 to 0.4 depending on model and size; a 2026 review attributes much of the spread to thermostat-induced finite-size effects (Lepri, Livi, Politi, arXiv:2602.15512).
Posed since: 1997