Magnetization properties of some quantum spin ladders

The experimental realization of various spin ladder systems has prompted their detailed theoretical investigations. Hen we study the evolution of ground-state magnetization with an external magnetic field for two different antiferromagnetic systems: a three-legged spin-1/2 ladder, and a two-legged spin-1/2 ladder with an additional diagonal interaction. The finite system density-matrix renormalization-group method is employed for numerical studies of the three-chain system, and an effective low-energy Hamiltonian is used in the limit of strong interchain coupling to study the two- and three-chain systems. The three-chain system has a magnetization plateau at one-third of the saturation magnetization. The two-chain system has a plateau at zero magnetization due to a gap above the singlet ground state. It also has a plateau at half of the saturation magnetization for a certain range of values of the couplings. We study the regions of transitions between plateaus numerically and analytically, and find that they are described, at first order in a strong-coupling expansion, by an XXZ spin-1/2 chain in a magnetic field; the second-order terms give corrections to the XXZ model, We also study numerically some low-temperature properties of the three-chain system, such as the magnetization, magnetic susceptibility and specific heat. [S0163-1829(99)303001-5].

Markov chains, R-trivial monoids and representation theory

We develop a general theory of Markov chains realizable as random walks on R-trivial monoids. It provides explicit and simple formulas for the eigenvalues of the transition matrix, for multiplicities of the eigenvalues via Mobius inversion along a lattice, a condition for diagonalizability of the transition matrix and some techniques for bounding the mixing time. In addition, we discuss several examples, such as Toom-Tsetlin models, an exchange walk for finite Coxeter groups, as well as examples previously studied by the authors, such as nonabelian sandpile models and the promotion Markov chain on posets. Many of these examples can be viewed as random walks on quotients of free tree monoids, a new class of monoids whose combinatorics we develop.

A finite variant of the Toom Model

We present results for a finite variant of the one-dimensional Toom model with closed boundaries. We show that the steady state distribution is not of product form, but is nonetheless simple. In particular, we give explicit formulas for the densities and some nearest neighbour correlation functions. We also give exact results for eigenvalues and multiplicities of the transition matrix using the theory of R-trivial monoids in joint work with A. Schilling, B. Steinberg and N. M. Thiery.

Nuclear weak interaction rates during stellar evolution and collapse

Nuclear weak interaction rates, including electron and positron emission rates, and continuum electron and positron capture rates , as well as the associated v and –/v energy loss rates are calculated on a detailed grid of temperature and density for the free nucleons and 226 nuclei with masses between A = 21 and 60. Gamow-Teller and Fermi discrete-state transition matrix element systematics and the Gamow-Teller T^< →/← T^> resonance transitions are discussed in depth and are implemented in the stellar rate calculations. Results of the calculations are presented on an abbreviated grid of temperature and density and comparison is made to terrestrial weak transition rates where possible. Neutron shell blocking of allowed electron capture on heavy nuclei during stellar core collapse is discussed along with several unblocking mechanisms operative at high temperature and density. The results of one-zone collapse calculations are presented which suggest that the effect of neutron shell blocking is to produce a larger core lepton fraction at neutrino trapping which leads to a larger inner-core mass and hence a stronger post-bounce shock.

Existence of the transverse relaxation time in optically excited bulk semiconductors

Two basic types of depolarization mechanisms, carrier-carrier (CC) and carrier-phonon (CP) scattering, are investigated in optically excited bulk semiconductors (3D), in which the existence of the transverse relaxation time is proven based on the vector property of the interband transition matrix elements. The dephasing rates for both CC and CP scattering are determined to be equal to one half of the total scattering-rate-integrals weighted by the factors (1 - cos chi), where chi are the scattering angles. Analytical expressions of the polarization dephasing due to CC scattering are established by using an uncertainty broadening approach, and analytical ones due to both the polar optical-phonon and non-polar deformation potential scattering (including inter-valley scattering) are also presented by using the sharp spectral functions in the dephasing rate calculations. These formulas, which reveal the trivial role of the Coulomb screening effect in the depolarization processes, are used to explain the experimental results at hand and provide a clear physical picture that is difficult to extract from numerical treatments.

The origin of the transverse relaxation time in optically excited semiconductor quantum wells

The origin of the transverse relaxation time in optically excited semiconductor quantum wells is investigated based on the vector property of the interband transition matrix elements. The dephasing rate due to carrier-carrier (CC) scattering is found to be equal to half of the common momentum relaxation rate. The analytical expression of the polarization dephasing due to CC scattering in two-dimension is established and the dependence of the dephasing rate Gamma(cc) on the carrier density N is determined to be Gamma(cc) = constant (.) N-1/2, which is used to explain the experimental results and provides a promising physical picture. (C) 2004 Elsevier B.V. All rights reserved.

Effects of Yb3+ in Er3+/Yb3+ codoped fluorophosphate glasses

For the Er3+/Yb3+ codoped fluorophosphate glasses, Judd-Ofelt theory is used to analyse the influence of YbF3 as not a sensitizer but an average component on the spectroscopic properties around 1530 nm emission. The double roles of Yb3+, as a sensitizer and as an average component, are discussed. It is found that Yb3+ as an average component contributes to the increase of fluorescence lifetime, and Yb3+ as a sensitizer has the best sensitization when its concentration is 2.4 mol%.

Growth of Skipjack tuna (Katsuwonus pelamis) in the eastern Pacific Ocean as estimated from tagging data

English: Data obtained from tagging experiments initiated during 1953-1958 and 1969-1981 for skipjack tuna from the coastal eastern Pacific Ocean (EPO) are reanalyzed, using the Schnute generalized growth model. The objective is to provide information that can be used to generate a growth transition matrix for use in a length-structured population dynamics model. The analysis includes statistical approaches to include individual variability in growth as a function of length at release and time at liberty, measurement error, and transcription error. The tagging data are divided into northern and southern regions, and the results suggest that growth rates differ between the two regions. The Schnute model provides a significantly better fit to the data than the von Bertalanffy model, a sub-model of the Schnute model, for the northern region, but not for the southern region. Individual variation in growth is best described as a function of time at liberty and as a function of growth increment for the northern and southern regions, respectively. Measurement error is a significant part of the total variation, but the results suggest that there is no bias caused by the measurement error. Additional information, particularly for small and large fish, is needed to produce an adequate growth transition matrix that can be used in a length-structured population dynamics model for skipjack tuna in the EPO. Spanish: Los datos obtenidos de los experimentos de marcado iniciados durante los períodos de 1953- 1958 y de 1969-1981 para el atún barrilete en las costas del Océano Pacífico Oriental (OPO) fueron analizados nuevamente, utilizando el modelo de crecimiento generalizado de Schnute. El objetivo es brindar información que sea útil para producir una matriz sobre la tran-sición de crecimiento que pueda utilizarse en un modelo de dinámica poblacional estructurado por talla. El análisis usa enfoques estadísticos para poder incluir la variabilidad individual del crecimiento como función de la talla de liberación y tiempo en libertad, el error de medición, y el error de transcripción. Los datos de marcado son divididos en regiones norte y sur, y los resultados sugieren que las tasas de crecimiento en las dos regiones son diferentes. En la región norte, pero no en la región sur, el modelo de Schnute se ajusta significativamente mejor a los datos que el modelo von Bertalanffy, un sub-modelo del modelo de Schnute. La mejor descripción de la variación individual en el crecimiento es como una función del tiempo en libertad y como una función del incremento de crecimiento para las regiones norte y sur, respectivamente. El error de medición es una parte significativa de la variación total, pero los resultados sugieren que no existe un sesgo causado por el error de medición. Se necesita información adicional, particularmente para peces pequeños y grandes, para poder producir una matriz de transición de crecimiento adecuada que pueda utilizarse en el modelo de dinámica poblacional estructurado por tallas para el atún barrilete en el OPO.

Impact of heterogeneous link qualities and network connectivity on binary consensus

In this paper we consider a network that is trying to reach consensus over the occurrence of an event while communicating over Additive White Gaussian Noise (AWGN) channels. We characterize the impact of different link qualities and network connectivity on consensus performance by analyzing both the asymptotic and transient behaviors. More specifically, we derive a tight approximation for the second largest eigenvalue of the probability transition matrix. We furthermore characterize the dynamics of each individual node. © 2009 AACC.

Electronic structure and optical gain of truncated InAs1-xNx/GaAs quantum dots

The shape of truncated square-based pyramid quantum dots (QDs) is similar to that of real QDs in experiments. The electronic band structures and optical gain of InAs1-xNx/GaAs QDs are calculated by using the 10-band k.p model, and the strain is calculated by the valence force field (VFF) method. When the top part of the QD is truncated, greater truncation corresponds to a flatter shape of the QD. The truncation changes the strain distribution and the confinement in the z direction. A flatter QD has a greater C1-HH1 transition energy, greater transition matrix element, less detrimental effect of higher excited transition, and higher saturation gain and differential gain. The trade-off between these properties must be considered. From our results, a truncated QD with half of its top part removed has better overall performance. This can provide guidance to growing QDs in experiments in which the proper growing conditions can be controlled to achieve required properties. (C) 2009 Elsevier Ltd. All rights reserved.

Electronic structure and optical properties of quantum rods with wurtzite structure

The Hamiltonian of the wurtzite quantum rods with an ellipsoidal boundary is given after a coordinate transformation. The energies, wave functions, and transition possibilities are obtained as functions of the aspect ratio e with the same method we used on spherical dots. With an overall consideration of both the transition matrix element and the Boltzmann distribution we explained why the polarization factor increases with increasing e and approaches a saturation value, which tallies quite well with the experimental result. When e increases more and more S-z states are mixed into the ground, second, and third states of J(z)=1/2, resulting in an increase of the emission of z polarization. It is just the linear terms of the momentum operator in the hole Hamiltonian that cause the mixing of S and P states in the hole ground state. The effects of the crystal field splitting energy, temperature, and transverse radius to the polarization are also considered. We also calculated the band gap variation with the size and shape of the quantum rods.

Electronic structures of cubic lattice quantum dots

In this article, we give the electronic structure and optical transition matrix elements of coupled quantum dots (QDs) arranged as different cubic lattices: simple cubic (sc), body-centered cubic (bcc), and face-centered cubic (fcc) superlattices. The results indicate that electron and hole energies of bcc, sc, and fcc superlattices are the lowest, the highest, and the middle, respectively, for the same subband under the same QD density or under the same superlattice constant. For a fixed QD density, the confinement effects in sc, fcc, and bcc superlattices are the strongest, the middle, and the weakest, respectively. There are only one, two, and four confined energy bands, with energies lower than the potential barrier for sc, bcc, and fcc QD superlattices, respectively. The results have great significance for researching and making semiconductor quantum dot devices. (C) 1998 American Institute of Physics. [S0021-8979(98)02119-7]

Quantum confinement effect in silicon quantum-well layers

The electronic states and optical transition properties of silicon quantum-well layers embedded by SiO2 layers are studied by the empirical pseudopotential homojunction model. The energy bands, wave functions, and the optical transition matrix elements are obtained for layers of thickness from 1 to 6 nm, and three oriented directions (001), (110), and (111). It is found that for Si layers in the (001) direction the energy gap is pseudodirect, for these in the (111) direction the energy gap is indirect, while for those in the (110) direction the energy gap is pseudodirect or indirect for a thickness smaller or larger than 3 nm, respectively. The optical transition matrix elements are smaller than that of diner transition, and increase with decreasing layer thickness. When the thickness of a layer is smaller than 2 nm, the Si QW layers have larger transition matrix elements. It is caused by mixing of bulk X states with the Gamma(1) state. The calculated results are compared with experimental results.

EFFECTIVE-MASS THEORY FOR GAAS/GA1-XALXAS QUANTUM WIRES AND CORRUGATED SUPERLATTICES GROWN ON (311)-ORIENTED SUBSTRATES

The electronic structures of GaAs/Ga1-xAlxAs quantum wires (corrugated superlattices) grown on (311)-oriented substrates are studied in the framework of the effective-mass envelope-function method. The electron and hole subband structure and optical transition matrix elements are calculated. When x=1, the results are compared with experiments, and it is found that the direct transition becomes an indirect transition as the widths of well and barrier become smaller.

THEORY OF THE ELECTRONIC-STRUCTURE OF POROUS SI

A theoretical model for the electronic structure of porous Si is presented. Three geometries of porous Si (wire with square cross section, pore with square cross section, and pore with circular cross section) along both the [001] and [110] directions are considered. It is found that the confinement geometry affects decisively the ordering of conduction-band states. Due to the quantum confinement effect, there is a mixing between the bulk X and GAMMA states, resulting in finite optical transition matrix elements, but smaller than the usual direct transition matrix elements by a factor of 10(-3). We found that the strengths of optical transitions are sensitive to the geometry of the structure. For (001) porous Si the structure with circular pores has much stronger optical transitions compared to the other two structures and it may play an important role in the observed luminescence. For this structure the energy difference between the direct and the indirect conduction-band minima is very small. Thus it is possible to observe photoluminescence from the indirect minimum at room temperature. For (110) porous Si of similar size of cross section the energy gap is smaller than that of (001) porous Si. The optical transitions for all three structures of (110) porous Si tend to be much stronger along the axis than perpendicular to the axis.