Resonant Interactions in the α -FPUT Lattice with Site-Dependent Coefficients

The wave turbulence framework has proven to be an effective tool for analyzing certain features of nonlinear energy transfer in one-dimensional nonlinear chains. In this work, we extend this approach to the $\alpha$ -FPUT problem when the spring stiffness $\chi$ and the nonlinear coefficient $\alpha$ are site-dependent. Although three-wave interactions are non-resonant for constant coefficients, their spatial modulation gives rise to a non-trivial resonant manifold. In this framework, we derive a new kinetic equation that suggests the possibility of substantially faster thermalization than in the constant-coefficient case. The new kinetic equation also includes an additional term that can be associated with the Bragg-scattering mechanism, which promotes the isotropization of the wave-action spectral density function. We corroborate these results with direct numerical simulations, confirming the radically faster thermalization pathway in the presence of random coefficients.