Properties of convergence of a class of iterative processes generated by sequences of self-mappings with applications to switched dynamic systems

This article investigates the convergence properties of iterative processes involving sequences of self-mappings of metric or Banach spaces. Such sequences are built from a set of primary self-mappings which are either expansive or non-expansive self-mappings and some of the non-expansive ones can be contractive including the case of strict contractions. The sequences are built subject to switching laws which select each active self-mapping on a certain activation interval in such a way that essential properties of boundedness and convergence of distances and iterated sequences are guaranteed. Applications to the important problem of stability of dynamic switched systems are also given.

Direct observation of coherent spin transfer processes in an InGaAs/GaAs quantum well via two-color time-resolved Kerr rotation measurements

A two-color time-resolved Kerr rotation spectroscopy system was built, with a femtosecond Ti:sapphire laser and a photonic crystal fiber, to study coherent spin transfer processes in an InGaAs/GaAs quantum well sample. The femtosecond Ti:sapphire laser plays two roles: besides providing a pump beam with a tunable wavelength, it also excites the photonic crystal fiber to generate supercontinuum light ranging from 500 nm to 1600 nm, from which a probe beam with a desirable wavelength is selected with a suitable interference filter. With such a system, we studied spin transfer processes between two semiconductors of different gaps in an InGaAs/GaAs quantum well sample. We found that electron spins generated in the GaAs barrier were transferred coherently into the InGaAs quantum well. A model based on rate equations and Bloch-Torrey equations is used to describe the coherent spin transfer processes quantitatively. With this model, we obtain an effective electron spin accumulation time of 21 ps in the InGaAs quantum well.