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

Expansion of pinched hypersurfaces of the Euclidean and hyperbolic space by high powers of curvature

We prove convergence results for expanding curvature flows in the Euclidean and hyperbolic space. The flow speeds have the form $F^{-p}$, where $p>1$ and $F$ is a positive, strictly monotone and 1-homogeneous curvature function. In particular this class includes the mean curvature $F=H$. We prove that a certain initial pinching condition is preserved and the properly rescaled hypersurfaces converge smoothly to the unit sphere. We show that an example due to Andrews-McCoy-Zheng can be used to construct strictly convex initial hypersurfaces, for which the inverse mean curvature flow to the power $p>1$ loses convexity, justifying the necessity to impose a certain pinching condition on the initial hypersurface.Comment: 18 pages. We included an example for the loss of convexity and pinching. In the third version we dropped the concavity assumption on F. Comments are welcom

Excitation and emission spectra of rubidium in rare-gas thin-films

To understand the optical properties of atoms in solid state matrices, the absorption, excitation and emission spectra of rubidium doped thin-films of argon, krypton and xenon were investigated in detail. A two-dimensional spectral analysis extends earlier reports on the excitation and emission properties of rubidium in rare-gas hosts. We found that the doped crystals of krypton and xenon exhibit a simple absorption-emission relation, whereas rubidium in argon showed more complicated spectral structures. Our sample preparation employed in the present work yielded different results for the Ar crystal, but our peak positions were consistent with the prediction based on the linear extrapolation of Xe and Kr data. We also observed a bleaching behavior in rubidium excitation spectra, which suggests a population transfer from one to another spectral feature due to hole-burning. The observed optical response implies that rubidium in rare-gas thin-films is detectable with extremely high sensitivity, possibly down to a single atom level, in low concentration samples.Comment: 7 pages, 5 figure

Strong extinction of a laser beam by a single molecule

We present an experiment where a single molecule strongly affects the amplitude and phase of a laser field emerging from a subwavelength aperture. We achieve a visibility of -6% in direct and +10% in cross-polarized detection schemes. Our analysis shows that a close to full extinction should be possible using near-field excitation.Comment: 5 pages, 4 figures, submitted to PR

Mean Curvature Flow of Spacelike Graphs

We prove the mean curvature flow of a spacelike graph in $(\Sigma_1\times \Sigma_2, g_1-g_2)$ of a map $f:\Sigma_1\to \Sigma_2$ from a closed Riemannian manifold $(\Sigma_1,g_1)$ with $Ricci_1> 0$ to a complete Riemannian manifold $(\Sigma_2,g_2)$ with bounded curvature tensor and derivatives, and with sectional curvatures satisfying $K_2\leq K_1$, remains a spacelike graph, exists for all time, and converges to a slice at infinity. We also show, with no need of the assumption $K_2\leq K_1$, that if $K_1>0$, or if $Ricci_1>0$ and $K_2\leq -c$, $c>0$ constant, any map $f:\Sigma_1\to \Sigma_2$ is trivially homotopic provided $f^*g_2<\rho g_1$ where $\rho=\min_{\Sigma_1}K_1/\sup_{\Sigma_2}K_2^+\geq 0$, in case $K_1>0$, and $\rho=+\infty$ in case $K_2\leq 0$. This largely extends some known results for $K_i$ constant and $\Sigma_2$ compact, obtained using the Riemannian structure of $\Sigma_1\times \Sigma_2$, and also shows how regularity theory on the mean curvature flow is simpler and more natural in pseudo-Riemannian setting then in the Riemannian one.Comment: version 5: Math.Z (online first 30 July 2010). version 4: 30 pages: we replace the condition $K_1\geq 0$ by the the weaker one $Ricci_1\geq 0$. The proofs are essentially the same. We change the title to a shorter one. We add an applicatio