Asymmetric Transport in Nonlinear Wave Chaos

The intrinsic dynamical complexity of classically chaotic systems enforces a universal statistical description of the transport properties of their wave-mechanical analogues. These universal rules have been established within the framework of linear wave transport, where non-linear interactions are omitted, and the superposition principle holds. Many of these laws are described using phenomenological theories, like Random Matrix Theory (RMT), and have been established using toy models, that maintain the generic features of wave-chaos. Here, using a nonlinear complex graph, we exploit both experimentally and theoretically the interplay of nonlinear interactions and wave chaos. Our focus is on asymmetric transport (AT), its universal bounds, and its statistical description via RMT which are controlled by the structural asymmetry factor (SAF) characterizing the structure of the graph. The latter dictates the asymmetric intensity range (AIR) within which an incident wave demonstrates AT when injected from different ports. The AIR increases, without necessarily deteriorating the AT when losses are introduced. Our research initiates the quest for universalities and their violations in wave transport of nonlinear chaotic systems and has potential applications for the design of magnetic-free isolators.