Friedel Oscillations in Carbon Nanotube Quantum Dots and Superlattices
Interface states of all-metallic carbon nanotube quantum dots and superlattices are studied within a tight-binding model. We focus on achiral systems made by connecting armchair (n, n) and zigzag (2n, 0) tubes with a full ring of n pentagon-heptagon topological defects. We show that the coupling between interface states, which arise from the topological defects, reflects the existence of the Friedel oscillations in the (n, n) tube, with an unusually large decay exponent. We expect this interaction to be important for the understanding of other physical properties, such as selective dot growth, magnetic interaction through carbon tubes or optical spectroscopy of interface states.
Abstract In this paper, a simplified congestion control model is considered to study the quasiperiodic motion induced by heterogenous time delays. Analysis for the stability of the equilibrium shows that the Hopf bifurcation curves with diverse frequencies may intersect at the so-called non-resonant double Hopf bifurcation point. Choosing the delays as the bifurcation parameters and employing the method of multiple scales, the amplitude–frequency equations or normal form equations are obtained theoretically. Based on these equations, the dynamics near the bifurcation point is classified. The values of the delays for which the quasiperiodic motion exists can be predicted with an acceptable accuracy. This result provides a reference in designing and optimizing the network systems.