Rectification in non-equilibrium gyroscopic networks

One of the goals of molecular engineering is to find design principles for rectification in microscopic conditions, which could lead to the fabrication microscopic motors. Past studies have successfully achieved rectifications in few-body or terminal systems, however, the extension to many-body system is not straightforward. We study energy rectification in a many-body model that combines the active bath and the gyroscopic metamaterials, and numerically and theoretically show that spontaneous heat rectification is achieved at the steady state. We then focus on understanding two issues: the mechanism of this rectification, and the relationship between the network geometry and the flow pattern. Given the knowledge of chiral eigenmodes in isolated gyroscopic networks, the rectification mechanism can be understood as a result of the weighted excitation of these modes. By expanding the heat flux as a summation over paths in the weak interaction regime, we can understand the flow pattern in a complex network from simple paths, which in turn enables us to control the rectification by the design of the network geometry.