Starting from a uniform d-wave superconducting phase we study the energy cost due to imposed unidirectional defects with a vanishing pairing amplitude. Both renormalized mean-field theory and variational Monte Carlo calculations within the t–J model yield that the energies of inhomogeneous and uniform phases are very close to each other. This suggests that small perturbations in the microscopic...

This paper gives a criterion for the non-vanishing of Dirac cohomology $\mathcal{L}_S(Z)$, where $\mathcal{L}_S(\cdot)$ is cohomological induction functor, while inducing module $Z$ irreducible, unitarizable, and in good range. As an application, we give formula counting number strings series. Using this formula, classify all irreducible unitary representations $E_{6(2)}$ with non-zero cohomolo...

We show that the Gauss-Bonnet term is the only consistent curvature squared interaction in the Randall-Sundrum model and various static and inflationary solutions can be found. And from metric perturbations around the RS background with a single brane embedded, we also show that for a vanishing Gauss-Bonnet coefficient, the brane bending allows us to reproduce the 4D Einstein gravity at the lin...

In this paper we study the effect of external perturbations on a networked control system. We start by assuming that the nonnetworked system without perturbation is exponentially stable. Then, for fast enough networks we show that if the perturbation is bounded the networked system is ultimately bounded and if the perturbation is vanishing then the networked system is asymptotically stable. We ...