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Plenary Talk: A wave turbulence approach to anomalous conduction in the FPUT chain

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HY2W04 - Statistical mechanics, integrability and dispersive hydrodynamics

One-dimensional particle chains are fundamental models to explain anomalous thermal conduction in low-dimensional solids. In these systems the thermal energy is carried by phonons. The average energy transfer between the phonons is described by the wave kinetic equation (WKE), formally derived directly from the microscopic dynamics. Here, I consider the spatially nonhomogeneous WKE for the FPUT model, with thermostats set to different temperatures at the two ends of the chain. Numerical simulations show that the anomalous scaling of the conductivity with the system size is well reproduced by the WKE . The anomalous conduction is the result of a nontrivial interplay between high and low wavenumbers: while the high-wavenumber phonons relax to local thermodynamic equilibrium transporting energy diffusively, à la Fourier, the low wavenumber phonons are nearly noninteracting and transfer energy ballistically.

This talk is part of the Isaac Newton Institute Seminar Series series.

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