Relaxation in time elapsed neuron network models in the weak connectivity regime

In order to describe the firing activity of a homogenous assembly of neurons, we consider time elapsed models, which give mathematical descriptions of the probability density of neurons structured by the distribution of times elapsed since the last discharge. Under general assumption on the firing rate and the delay distribution, we prove the uniqueness of the steady state and its nonlinear exponential stability in the weak connectivity regime. The result generalizes some similar results obtained in [10] in the case without delay. Our approach uses the spectral analysis theory for semigroups in Banach spaces developed recently by the first author and collaborators

Intense terahertz laser fields on a quantum dot with Rashba spin-orbit coupling

We investigate the effects of the intense terahertz laser field and the spin-orbit coupling on single electron spin in a quantum dot. The laser field and the spin-orbit coupling can strongly affect the electron density of states and can excite a magnetic moment. The direction of the magnetic moment depends on the symmetries of the system, and its amplitude can be tuned by the strength and frequency of the laser field as well as the spin-orbit coupling.Comment: 5 pages, 4 figures, to be published in J. Appl. Phy