Deterministic many-body dynamics with multifractal response - Yusuf Kasim; Tomaž Prosen (Physical Review Research)
Dynamical systems can display a plethora of ergodic and ergodicity breaking behaviors, ranging from simple periodicity to ergodicity and chaos. Here we report an unusual type of nonergodic behavior in a many-body discrete-time dynamical system, specifically a multiperiodic response with multifractal distribution of equilibrium spectral weights at all rational frequencies. This phenomenon is observed in the momentum-conserving variant of the newly introduced class of the so-called parity check reversible cellular automata, which we define with respect to an arbitrary bipartite lattice. Although the models display strong fragmentation of phase space of configurations, we demonstrate that the effect qualitatively persists within individual fragmented sectors, and even individual typical many-body trajectories. We provide detailed numerical analysis of examples on 2D (honeycomb, square) and 3D (cubic) lattices.