FPU physics with nanomechanical graphene resonators: intrinsic relaxation and thermalization from flexural mode coupling

Thermalization in nonlinear systems is a central concept in statistical mechanics and has been extensively studied theoretically since the seminal work of Fermi, Pasta and Ulam (FPU). Using molecular dynamics and continuum modeling of a ring-down setup, we show that thermalization due to nonlinear mode coupling intrinsically limits the quality factor of nanomechanical graphene drums and turns them into potential test beds for FPU physics. We find the thermalization rate $\Gamma$ to be independent of radius and scaling as $\Gamma\sim T^*/\epsilon_{{\rm pre}}^2$, where $T^*$ and $\epsilon_{{\rm pre}}$ are effective resonator temperature and prestrain.