Universal nonadiabatic energy pumping in a quasiperiodically driven extended system

The paradigm of Floquet engineering topological states matter can be generalized into the time-quasiperiodic scenario, where a lower dimensional time-dependent system maps higher one by combining physical dimensions with additional synthetic generated multiple incommensurate driving frequencies. Different than most previous works in which gapped phases were considered, we propose an experimentally realizable, chain driven two frequencies, gapless Weyl semimetal dimension. Based on analytical reasoning and numerical simulations, found nonadiabatic quantum dynamics this exhibit energy pumping behaviors characterized universal functions. We also numerically such are robust against considerable amount spatial disorder.