Electron Spin Decoherence in Bulk and Quantum Well Zincblende Semiconductors

A theory for longitudinal (T1) and transverse (T2) electron spin coherence times in zincblende semiconductor quantum wells is developed based on a non-perturbative nanostructure model solved in a fourteen-band restricted basis set. Distinctly different dependences of coherence times on mobility, quantization energy, and temperature are found from previous calculations. Quantitative agreement between our calculations and measurements is found for GaAs/AlGaAs, InGaAs/InP, and GaSb/AlSb quantum wells.Comment: 11 pages, 3 figure

Anisotropic splitting of intersubband spin plasmons in quantum wells with bulk and structural inversion asymmetry

In semiconductor heterostructures, bulk and structural inversion asymmetry and spin-orbit coupling induce a k-dependent spin splitting of valence and conduction subbands, which can be viewed as being caused by momentum-dependent crystal magnetic fields. This paper studies the influence of these effective magnetic fields on the intersubband spin dynamics in an asymmetric n-type GaAs/AlGaAs quantum well. We calculate the dispersions of intersubband spin plasmons using linear response theory. The so-called D'yakonov-Perel' decoherence mechanism is inactive for collective intersubband excitations, i.e., crystal magnetic fields do not lead to decoherence of spin plasmons. Instead, we predict that the main signature of bulk and structural inversion asymmetry in intersubband spin dynamics is a three-fold, anisotropic splitting of the spin plasmon dispersion. The importance of many-body effects is pointed out, and conditions for experimental observation with inelastic light scattering are discussed.Comment: 8 pages, 6 figure

Turing instabilities in a mathematical model for signaling networks

GTPase molecules are important regulators in cells that continuously run through an activation/deactivation and membrane-attachment/membrane-detachment cycle. Activated GTPase is able to localize in parts of the membranes and to induce cell polarity. As feedback loops contribute to the GTPase cycle and as the coupling between membrane-bound and cytoplasmic processes introduces different diffusion coefficients a Turing mechanism is a natural candidate for this symmetry breaking. We formulate a mathematical model that couples a reaction-diffusion system in the inner volume to a reaction-diffusion system on the membrane via a flux condition and an attachment/detachment law at the membrane. We present a reduction to a simpler non-local reaction-diffusion model and perform a stability analysis and numerical simulations for this reduction. Our model in principle does support Turing instabilities but only if the lateral diffusion of inactivated GTPase is much faster than the diffusion of activated GTPase.Comment: 23 pages, 5 figures; The final publication is available at http://www.springerlink.com http://dx.doi.org/10.1007/s00285-011-0495-

Practical probabilistic programming with monads

The machine learning community has recently shown a lot of interest in practical probabilistic programming systems that target the problem of Bayesian inference. Such systems come in different forms, but they all express probabilistic models as computational processes using syntax resembling programming languages. In the functional programming community monads are known to offer a convenient and elegant abstraction for programming with probability distributions, but their use is often limited to very simple inference problems. We show that it is possible to use the monad abstraction to construct probabilistic models for machine learning, while still offering good performance of inference in challenging models. We use a GADT as an underlying representation of a probability distribution and apply Sequential Monte Carlo-based methods to achieve efficient inference. We define a formal semantics via measure theory. We demonstrate a clean and elegant implementation that achieves performance comparable with Anglican, a state-of-the-art probabilistic programming system.The first author is supported by EPSRC and the Cambridge Trust.This is the author accepted manuscript. The final version is available from ACM via http://dx.doi.org/10.1145/2804302.280431

Spin-orbit terms in multi-subband electron systems: A bridge between bulk and two-dimensional Hamiltonians

We analyze the spin-orbit terms in multi-subband quasi-two-dimensional electron systems, and how they descend from the bulk Hamiltonian of the conduction band. Measurements of spin-orbit terms in one subband alone are shown to give incomplete information on the spin-orbit Hamiltonian of the system. They should be complemented by measurements of inter-subband spin-orbit matrix elements. Tuning electron energy levels with a quantizing magnetic field is proposed as an experimental approach to this problem.Comment: Typos noticed in the published version have been corrected and several references added. Published in the special issue of Semiconductors in memory of V.I. Pere

Two-photon spin injection in semiconductors

A comparison is made between the degree of spin polarization of electrons excited by one- and two-photon absorption of circularly polarized light in bulk zincblende semiconductors. Time- and polarization-resolved experiments in (001)-oriented GaAs reveal an initial degree of spin polarization of 49% for both one- and two-photon spin injection at wavelengths of 775 and 1550 nm, in agreement with theory. The macroscopic symmetry and microscopic theory for two-photon spin injection are reviewed, and the latter is generalized to account for spin-splitting of the bands. The degree of spin polarization of one- and two-photon optical orientation need not be equal, as shown by calculations of spectra for GaAs, InP, GaSb, InSb, and ZnSe using a 14x14 k.p Hamiltonian including remote band effects. By including the higher conduction bands in the calculation, cubic anisotropy and the role of allowed-allowed transitions can be investigated. The allowed-allowed transitions do not conserve angular momentum and can cause a high degree of spin polarization close to the band edge; a value of 78% is calculated in GaSb, but by varying the material parameters it could be as high as 100%. The selection rules for spin injection from allowed-allowed transitions are presented, and interband spin-orbit coupling is found to play an important role.Comment: 12 pages including 7 figure

Method of Preparing Silica Absorbents

In the manufacture of phosphate fertilizer, compounds of fluorine are evolved. The amount of fluorine occurring in the phosphate rock used each year in the United States is about 8000 tons. It is proposed to utilize this material industrially. If the tower gases are passed through the water, reaction 3 SiF4 + 3 H2O → H2Sio3 + 2 H2SiF6 takes place. The solution is treated to recover the silicon fluoride as MgSiF4. The precipitated silicic acid is filtered out, dried and has good adsorptive properties. The adsorption value depends upon the acidity and other conditions. The silica obtained has better adsorption properties than Silica Gel

The prescribed mean curvature equation in weakly regular domains

We show that the characterization of existence and uniqueness up to vertical translations of solutions to the prescribed mean curvature equation, originally proved by Giusti in the smooth case, holds true for domains satisfying very mild regularity assumptions. Our results apply in particular to the non-parametric solutions of the capillary problem for perfectly wetting fluids in zero gravity. Among the essential tools used in the proofs, we mention a \textit{generalized Gauss-Green theorem} based on the construction of the weak normal trace of a vector field with bounded divergence, in the spirit of classical results due to Anzellotti, and a \textit{weak Young's law} for $(\Lambda,r_{0})$-minimizers of the perimeter.Comment: 23 pages, 1 figure --- The results on the weak normal trace of vector fields have been now extended and moved in a self-contained paper available at: arXiv:1708.0139