Curvature estimates for Weingarten hypersurfaces in Riemannian manifolds

We prove curvature estimates for general curvature functions. As an application we show the existence of closed, strictly convex hypersurfaces with prescribed curvature $F$, where the defining cone of $F$ is \C_+. $F$ is only assumed to be monotone, symmetric, homogeneous of degree 1, concave and of class C^{m,\al}, $m\ge4$.Comment: 9 pages, v2:final version, to be publishe

Combining gravity with the forces of the standard model on a cosmological scale

We prove the existence of a spectral resolution of the Wheeler-DeWitt equation when the underlying spacetime is a Friedman universe with flat spatial slices and where the matter fields are comprised of the strong interaction, with \SU(3) replaced by a general \SU(n), $n\ge 2$, and the electro-weak interaction. The wave functions are maps from $\R[4n+10]$ to a subspace of the antisymmetric Fock space, and one noteworthy result is that, whenever the electro-weak interaction is involved, the image of an eigenfunction is in general not one dimensional, i.e., in general it makes no sense specifying a fermion and looking for an eigenfunction the range of which is contained in the one dimensional vector space spanned by the fermion.Comment: 53 pages, v6: some typos correcte

Critical properties of the one-dimensional spin-1/2 antiferromagnetic Heisenberg model in the presence of a uniform field

In the presence of a uniform field the one-dimensional spin-$\frac{1}{2}$ antiferromagnetic Heisenberg model develops zero frequency excitations at field-dependent 'soft mode' momenta. We determine three types of critical quantities, which we extract from the finite-size dependence of the lowest excitation energies, the singularities in the static structure factors and the infrared singularities in the dynamical structure factors at the soft mode momenta. We also compare our results with the predictions of conformal field theory.Comment: 12 pages, REVTEX, 7 figures, submitted to Physical Review

Ultrafast circular polarization oscillations in spin-polarized vertical-cavity surface-emitting laser devices

Spin-polarized lasers offer new encouraging possibilities for future devices. We investigate the polarization dynamics of electrically pumped vertical-cavity surface-emitting lasers after additional spin injection at room temperature. We find that the circular polarization degree exhibits faster dynamics than the emitted light. Moreover the experimental results demonstrate a strongly damped ultrafast circular polarization oscillation due to spin injection with an oscillation frequency of approximately 11GHz depending on the birefringence in the VCSEL device. We compare our experimental results with theoretical calculations based on rate-equations. This allows us to predict undamped long persisting ultrafast polarization oscillations, which reveal the potential of spin-VCSELs for ultrafast modulation applications

Birefringence controlled room-temperature picosecond spin dynamics close to the threshold of vertical-cavity surface-emitting laser devices

We analyze the spin-induced circular polarization dynamics at the threshold of vertical-cavity surface-emitting lasers at room-temperature using a hybrid excitation combining electrically pumping without spin preference and spin-polarized optical injection. After a short pulse of spin-polarized excitation, fast oscillations of the circular polarization degree (CPD) are observed within the relaxation oscillations. A theoretical investigation of this behavior on the basis of a rate equation model shows that these fast oscillations of CPD could be suppressed by means of a reduction of the birefringence of the laser cavity