Title: Yield in Amorphous Solids: The Ant in the Energy Landscape Labyrinth,
Abstract: It has recently been shown that yield in amorphous solids under oscillatory
shear is a dynamical transition from asymptotically periodic to asymptotically
chaotic, diffusive dynamics. However, the type and universality class of this
transition are still undecided. Here we show that the diffusive behavior of the
vector of coordinates of the particles comprising an amorphous solid when
subject to oscillatory shear, is analogous to that of a particle diffusing in a
percolating lattice, the so-called "ant in the labyrinth" problem, and that
yield corresponds to a percolation transition in the lattice. We explain this
as a transition in the connectivity of the energy landscape, which affects the
phase-space regions accessible to the coordinate vector for a given maximal
strain amplitude. This transition provides a natural explanation to the
observed limit-cycles, periods larger than one and diverging time-scales at
yield.