Dynamical decoupling noise spectroscopy

Decoherence is one of the most important obstacles that must be overcome in quantum information processing. It depends on the qubit-environment coupling strength, but also on the spectral composition of the noise generated by the environment. If the spectral density is known, fighting the effect of decoherence can be made more effective. Applying sequences of inversion pulses to the qubit system, we generate effective filter functions that probe the environmental spectral density. Comparing different pulse sequences, we recover the complete spectral density function and distinguish different contributions to the overall decoherence.Comment: 4+ pages, 3 figures. New experimental data was added. New references adde

The p-Laplace equation in domains with multiple crack section via pencil operators

The p-Laplace equation \n \cdot (|\n u|^n \n u)=0 \whereA n>0, in a bounded domain \O \subset \re^2, with inhomogeneous Dirichlet conditions on the smooth boundary \p \O is considered. In addition, there is a finite collection of curves \Gamma = \Gamma_1\cup...\cup\Gamma_m \subset \O, \quad \{on which we assume homogeneous Dirichlet boundary conditions} \quad u=0, modeling a multiple crack formation, focusing at the origin 0 \in \O. This makes the above quasilinear elliptic problem overdetermined. Possible types of the behaviour of solution $u(x,y)$ at the tip 0 of such admissible multiple cracks, being a "singularity" point, are described, on the basis of blow-up scaling techniques and a "nonlinear eigenvalue problem". Typical types of admissible cracks are shown to be governed by nodal sets of a countable family of nonlinear eigenfunctions, which are obtained via branching from harmonic polynomials that occur for $n=0$. Using a combination of analytic and numerical methods, saddle-node bifurcations in $n$ are shown to occur for those nonlinear eigenvalues/eigenfunctions.Comment: arXiv admin note: substantial text overlap with arXiv:1310.065