Carrier dynamics and coherent acoustic phonons in nitride heterostructures

We model generation and propagation of coherent acoustic phonons in piezoelectric InGaN/GaN multi-quantum wells embedded in a \textit{pin} diode structure and compute the time resolved reflectivity signal in simulated pump-probe experiments. Carriers are created in the InGaN wells by ultrafast pumping below the GaN band gap and the dynamics of the photoexcited carriers is treated in a Boltzmann equation framework. Coherent acoustic phonons are generated in the quantum well via both deformation potential electron-phonon and piezoelectric electron-phonon interaction with photogenerated carriers, with the latter mechanism being the dominant one. Coherent longitudinal acoustic phonons propagate into the structure at the sound speed modifying the optical properties and giving rise to a giant oscillatory differential reflectivity signal. We demonstrate that coherent optical control of the differential reflectivity can be achieved using a delayed control pulse.Comment: 14 pages, 11 figure

Classical Topological Order in Kagome Ice

We examine the onset of classical topological order in a nearest-neighbor kagome ice model. Using Monte Carlo simulations, we characterize the topological sectors of the groundstate using a non-local cut measure which circumscribes the toroidal geometry of the simulation cell. We demonstrate that simulations which employ global loop updates that are allowed to wind around the periodic boundaries cause the topological sector to fluctuate, while restricted local loop updates freeze the simulation into one topological sector. The freezing into one topological sector can also be observed in the susceptibility of the real magnetic spin vectors projected onto the kagome plane. The ability of the susceptibility to distinguish between fluctuating and non-fluctuating topological sectors should motivate its use as a local probe of topological order in a variety of related model and experimental systems.Comment: 17 pages, 9 figure

Polarization properties and dispersion relations for spiral resonances of a dielectric rod

Dielectric microcavities based on cylindrical and deformed cylindrical shapes have been employed as resonators for microlasers. Such systems support spiral resonances with finite momentum along the cylinder axis. For such modes the boundary conditions do not separate and simple TM and TE polarization states do not exist. We formulate a theory for the dispersion relations and polarization properties of such resonances for an infinite dielectric rod of arbitrary cross-section and then solve for these quantities for the case of a circular cross-section (cylinder). Useful analytic formulas are obtained using the eikonal (Einstein-Brillouin-Keller) method which are shown to be excellent approximations to the exact results from the wave equation. The major finding is that the polarization of the radiation emitted into the far-field is linear up to a polarization critical angle (PCA) at which it changes to elliptical. The PCA always lies between the Brewster and total-internal-reflection angles for the dielectric, as is shown by an analysis based on the Jones matrices of the spiraling rays.Comment: submitted to JOSA

The mean curvature of cylindrically bounded submanifolds

We give an estimate of the mean curvature of a complete submanifold lying inside a closed cylinder $B(r)\times\R^{\ell}$ in a product Riemannian manifold $N^{n-\ell}\times\R^{\ell}$. It follows that a complete hypersurface of given constant mean curvature lying inside a closed circular cylinder in Euclidean space cannot be proper if the circular base is of sufficiently small radius. In particular, any possible counterexample to a conjecture of Calabion complete minimal hypersurfaces cannot be proper. As another application of our method, we derive a result about the stochastic incompleteness of submanifolds with sufficiently small mean curvature.Comment: First version (December 2008). Final version, including new title (February 2009). To appear in Mathematische Annale

Regularity of Kobayashi metric

We review some recent results on existence and regularity of Monge-Amp\`ere exhaustions on the smoothly bounded strongly pseudoconvex domains, which admit at least one such exhaustion of sufficiently high regularity. A main consequence of our results is the fact that the Kobayashi pseudo-metric k on an appropriare open subset of each of the above domains is actually a smooth Finsler metric. The class of domains to which our result apply is very large. It includes for instance all smoothly bounded strongly pseudoconvex complete circular domains and all their sufficiently small deformations.Comment: 14 pages, 8 figures - The previously announced main result had a gap. In this new version the corrected statement is given. To appear on the volume "Geometric Complex Analysis - Proceedings of KSCV 12 Symposium

Quantum Cosmology for a Quadratic Theory of Gravity

For pure fourth order (${\cal{L}} \propto R^2$) quantum cosmology the Wheeler-DeWitt equation is solved exactly for the closed homogeneous and isotropic model. It is shown that by imposing as boundary condition that $\Psi = 0$ at the origin of the universe the wave functions behave as suggested by Vilenkin.Comment: 13 pages, latex,no figure

Resonant Coherent Phonon Spectroscopy of Single-Walled Carbon Nanotubes

Using femtosecond pump-probe spectroscopy with pulse shaping techniques, one can generate and detect coherent phonons in chirality-specific semiconducting single-walled carbon nanotubes. The signals are resonantly enhanced when the pump photon energy coincides with an interband exciton resonance, and analysis of such data provides a wealth of information on the chirality-dependence of light absorption, phonon generation, and phonon-induced band structure modulations. To explain our experimental results, we have developed a microscopic theory for the generation and detection of coherent phonons in single-walled carbon nanotubes using a tight-binding model for the electronic states and a valence force field model for the phonons. We find that the coherent phonon amplitudes satisfy a driven oscillator equation with the driving term depending on photoexcited carrier density. We compared our theoretical results with experimental results on mod 2 nanotubes and found that our model provides satisfactory overall trends in the relative strengths of the coherent phonon signal both within and between different mod 2 families. We also find that the coherent phonon intensities are considerably weaker in mod 1 nanotubes in comparison with mod~2 nanotubes, which is also in excellent agreement with experiment.Comment: 21 pages, 22 figure

The Random Discrete Action for 2-Dimensional Spacetime

A one-parameter family of random variables, called the Discrete Action, is defined for a 2-dimensional Lorentzian spacetime of finite volume. The single parameter is a discreteness scale. The expectation value of this Discrete Action is calculated for various regions of 2D Minkowski spacetime. When a causally convex region of 2D Minkowski spacetime is divided into subregions using null lines the mean of the Discrete Action is equal to the alternating sum of the numbers of vertices, edges and faces of the null tiling, up to corrections that tend to zero as the discreteness scale is taken to zero. This result is used to predict that the mean of the Discrete Action of the flat Lorentzian cylinder is zero up to corrections, which is verified. The ``topological'' character of the Discrete Action breaks down for causally convex regions of the flat trousers spacetime that contain the singularity and for non-causally convex rectangles.Comment: 20 pages, 10 figures, Typos correcte