Volumes of Compact Manifolds

We present a systematic calculation of the volumes of compact manifolds which appear in physics: spheres, projective spaces, group manifolds and generalized flag manifolds. In each case we state what we believe is the most natural scale or normalization of the manifold, that is, the generalization of the unit radius condition for spheres. For this aim we first describe the manifold with some parameters, set up a metric, which induces a volume element, and perform the integration for the adequate range of the parameters; in most cases our manifolds will be either spheres or (twisted) products of spheres, or quotients of spheres (homogeneous spaces). Our results should be useful in several physical instances, as instanton calculations, propagators in curved spaces, sigma models, geometric scattering in homogeneous manifolds, density matrices for entangled states, etc. Some flag manifolds have also appeared recently as exceptional holonomy manifolds; the volumes of compact Einstein manifolds appear in String theory.Comment: 26 pages, no figures; updated addresses and bibliography. To be published in Rep. Math. Phy

Wigner Functions for Arbitrary Quantum Systems

The possibility of constructing a complete, continuous Wigner function for any quantum system has been a subject of investigation for over 50 years. A key system that has served to illustrate the difficulties of this problem has been an ensemble of spins. Here we present a general and consistent framework for constructing Wigner functions exploiting the underlying symmetries in the physical system at hand. The Wigner function can be used to fully describe any quantum system of arbitrary dimension or ensemble size.Comment: 5 pages, 3 figure

Calculation of the unitary part of the Bures measure for N-level quantum systems

We use the canonical coset parameterization and provide a formula with the unitary part of the Bures measure for non-degenerate systems in terms of the product of even Euclidean balls. This formula is shown to be consistent with the sampling of random states through the generation of random unitary matrices

Charged Higgs bosons from the 3-3-1 models and the R(D(∗))\mathcal{R}(D^{(*)}) anomalies

Several anomalies in the semileptonic B-meson decays such as $\mathcal{R}(D^{(*)})$ have been reported by $BABAR$, Belle, and LHCb collaborations recently. In this paper, we investigate the contributions of the charged Higgs bosons from the 3-3-1 models to the $\mathcal{R}(D^{(*)})$ anomalies. We find that, in a wide range of parameter space, the 3-3-1 models might give reasonable explanations to the $\mathcal{R}(D^{(*)})$ anomalies and other analogous anomalies of the B meson's semileptonic decays.Comment: Accpeted by Physical Review

Analysis of the performance of InAs/InP(100) quantum dot waveguide photodetectors using a rate quation model

In this contribution we present a rate equation model for the simulation of InAs/InP(100) quantum dots which are used as the active material of waveguide photodetectors. Unlike the normal rate equation models in literature which are built for carrier injection and photon emission, our model is modified for the carrier extraction and photon absorption. The simulation results are compared with previous experimental results. Experimental observations are explained in terms of fundamental properties of the quantum dots, e.g. the bias voltage dependent carrier extraction rate and absorption coefficient

Observation and modeling of long-wavelength InAs/InP (100) quantum dot amplifier small signal gain spectra

Measured gain spectra from InAs/InP (100) quantum-dot amplifiers have been analyzed with a quantum-dot rate-equation model. The amplifiers are fabricated to have a peak gain wavelength around 1700nm. Our comparison between measured and simulated gain spectra shows that two effects in the quantum-dot material introduce the 65 nm blue shift and change in shape that have been observed in the measured gain spectrum with an increase in injection current density from 1000A/cm2 to 3000A/cm2. The first effect is the shift from GS to ES, and the second effect the dot size dependent filling due to the dot size dependent escape rates