Scaling laws for the bifurcation escape rate in a nanomechanical resonator.

We report on experimental and theoretical studies of the fluctuation-induced escape time from a metastable state of a nanomechanical Duffing resonator in a cryogenic environment. By tuning in situ the nonlinear coefficient γ we could explore a wide range of the parameter space around the bifurcation point, where the metastable state becomes unstable. We measured in a relaxation process the distribution of the escape times. We have been able to verify its exponential distribution and extract the escape rate Γ. We investigated the scaling of Γ with respect to the distance to the bifurcation point and γ, finding an unprecedented quantitative agreement with the theoretical description of the stochastic problem. Simple power scaling laws turn out to hold in a large region of the parameter space, as anticipated by recent theoretical predictions. These unique findings, implemented in a model dynamical system, are relevant to all systems experiencing underdamped saddle-node bifurcation.

Detection of local-moment formation using the resonant interaction between coupled quantum wires.

We study the influence of many-body interactions on the transport characteristics of a pair of quantum wires that are coupled to each other by means of a quantum dot. Under conditions where a local magnetic moment is formed in one of the wires, tunnel coupling to the other gives rise to an associated peak in its density of states, which can be detected directly in a conductance measurement. Our theory is therefore able to account for the key observations in the recent study of T. Morimoto et al. [Appl. Phys. Lett., ()]], and demonstrates that coupled quantum wires may be used as a system for the detection of local magnetic-moment formation.