Nonreciprocity and nonlinearity: Applications in complex plasmas and time series

Abstract

Newton's third law of action and reaction is one pillar of classical mechanics. In nonequilibrium systems this fundamental law can be broken when the effective interaction is mediated by a third body, enabling surprising and counterintuitive effects. In a similar manner, the discovery of deterministic chaos in nonlinear systems enriched the field of time series analysis. This thesis covers dynamical effects based on nonreciprocal interactions in complex plasmas and sheds a light on the role of the Fourier phases in nonlinear time series. In a complex plasma, which consists of charged microparticles immersed in a weakly ionized gas, streaming ions can play the role of the third body in the microparticle interaction. As a first nonreciprocity effect, the asymmetric triggering of the mode-coupling instability, where some wave modes in a two-dimensional plasma crystal grow exponentially with time, is studied in molecular-dynamics simulations. It is shown that an anisotropic confinement in the horizontal plane can trigger the instability in only two or four out of the six directions that are allowed in the hexagonal crystal lattice. In very good agreement with previous experimental observations, the asymmetric triggering of the instability is accompanied by a synchronized motion of the particles. A novel order parameter is developed to quantify the direction-dependent synchronization pattern. Possible mechanisms leading to a more delicate symmetry breaking that cannot be explained by the anisotropic confinement are also discussed. A second effect based on nonreciprocal particle interactions is the channeling mechanism, where an extra particle that is not part of the two-dimensional crystal lattice floats slightly above the crystal and moves with almost constant velocity through a channel formed by the lattice. The mechanism is reproduced in simulations. It is shown that due to the nonreciprocity of the interactions, the extra particle attracts nearby particles, while it is itself repelled from the approaching particles, leading to a self-propelled motion of the extra particle. A simple theoretical model for the propulsion is provided which predicts the velocity of the extra particle. The fact that all nonlinearities of a time series reside in the Fourier phases is implicitly used in many schemes for generating surrogates, but has not received much attention beyond that. Here, correlations in the Fourier phases are shown to have an impact on the nonlinear properties of a time series. Spurious phase correlations in amplitude-adjusted surrogates, that should be devoid of nonlinear information, can in turn lead to a nondetection of nonlinearity. Finally, by comparing different nonlinearity measures, the nonlinear prediction error is found to be superior to more recent measures derived from network theory.