Obstructions to Fibering a Manifold

Given a map f: M \to M of closed topological manifolds we define torsion obstructions whose vanishing is a necessary condition for f being homotopy equivalent to a projection of a locally trivial fiber bundle. If N = S^1, these torsion obstructions are identified with the ones due to Farrell. We have changed the exposition according to the comments of the referee and corrected some typos. The paper will appear in Geometriae Dedicata.Comment: 33 page

Continuous stochastic Schrodinger equations and localization

The set of continuous norm-preserving stochastic Schrodinger equations associated with the Lindblad master equation is introduced. This set is used to describe the localization properties of the state vector toward eigenstates of the environment operator. Particular focus is placed on determining the stochastic equation which exhibits the highest rate of localization for wide open systems. An equation having such a property is proposed in the case of a single non-hermitian environment operator. This result is relevant to numerical simulations of quantum trajectories where localization properties are used to reduce the number of basis states needed to represent the system state, and thereby increase the speed of calculation.Comment: 18 pages in LaTeX + 6 figures (postscript), uses ioplppt.sty. To appear in J. Phys.

Quantum chaos in open systems: a quantum state diffusion analysis

Except for the universe, all quantum systems are open, and according to quantum state diffusion theory, many systems localize to wave packets in the neighborhood of phase space points. This is due to decoherence from the interaction with the environment, and makes the quasiclassical limit of such systems both more realistic and simpler in many respects than the more familiar quasiclassical limit for closed systems. A linearized version of this theory leads to the correct classical dynamics in the macroscopic limit, even for nonlinear and chaotic systems. We apply the theory to the forced, damped Duffing oscillator, comparing the numerical results of the full and linearized equations, and argue that this can be used to make explicit calculations in the decoherent histories formalism of quantum mechanics.Comment: 18 pages standard LaTeX + 9 figures; extensively trimmed; to appear in J. Phys.

Artificial reefs: from ecological processes to fishing enhancement tools

info:eu-repo/semantics/publishedVersio

Quantum trajectories for Brownian motion

We present the stochastic Schroedinger equation for the dynamics of a quantum particle coupled to a high temperature environment and apply it the dynamics of a driven, damped, nonlinear quantum oscillator. Apart from an initial slip on the environmental memory time scale, in the mean, our result recovers the solution of the known non-Lindblad quantum Brownian motion master equation. A remarkable feature of our approach is its localization property: individual quantum trajectories remain localized wave packets for all times, even for the classically chaotic system considered here, the localization being stronger the smaller $\hbar$.Comment: 4 pages, 3 eps figure

Theoretical study of the insulating oxides and nitrides: SiO2, GeO2, Al2O3, Si3N4, and Ge3N4

An extensive theoretical study is performed for wide bandgap crystalline oxides and nitrides, namely, SiO_{2}, GeO_{2}, Al_{2}O_{3}, Si_{3}N_{4}, and Ge_{3}N_{4}. Their important polymorphs are considered which are for SiO_{2}: $\alpha$-quartz, $\alpha$- and $\beta$-cristobalite and stishovite, for GeO_{2}: $\alpha$-quartz, and rutile, for Al_{2}O_{3}: $\alpha$-phase, for Si_{3}N_{4} and Ge_{3}N_{4}: $\alpha$- and $\beta$-phases. This work constitutes a comprehensive account of both electronic structure and the elastic properties of these important insulating oxides and nitrides obtained with high accuracy based on density functional theory within the local density approximation. Two different norm-conserving \textit{ab initio} pseudopotentials have been tested which agree in all respects with the only exception arising for the elastic properties of rutile GeO_{2}. The agreement with experimental values, when available, are seen to be highly satisfactory. The uniformity and the well convergence of this approach enables an unbiased assessment of important physical parameters within each material and among different insulating oxide and nitrides. The computed static electric susceptibilities are observed to display a strong correlation with their mass densities. There is a marked discrepancy between the considered oxides and nitrides with the latter having sudden increase of density of states away from the respective band edges. This is expected to give rise to excessive carrier scattering which can practically preclude bulk impact ionization process in Si_{3}N_{4} and Ge_{3}N_{4}.Comment: Published version, 10 pages, 8 figure

Single-electron measurements with a micromechanical resonator

A mechanical electroscope based on a change in the resonant frequency of a cantilever one micron in size in the presence of charge has recently been fabricated. We derive the decoherence rate of a charge superposition during measurement with such a device using a master equation theory adapted from quantum optics. We also investigate the information produced by such a measurement, using a quantum trajectory approach. Such instruments could be used in mesoscopic electronic systems, and future solid-state quantum computers, so it is useful to know how they behave when used to measure quantum superpositions of charge

Identification of CIITA Regulated Genetic Module Dedicated for Antigen Presentation

The class II trans-activator CIITA is a transcriptional co-activator required for the expression of Major Histocompatibility Complex (MHC) genes. Although the latter function is well established, the global target-gene specificity of CIITA had not been defined. We therefore generated a comprehensive list of its target genes by performing genome-wide scans employing four different approaches designed to identify promoters that are occupied by CIITA in two key antigen presenting cells, B cells and dendritic cells. Surprisingly, in addition to MHC genes, only nine new targets were identified and validated by extensive functional and expression analysis. Seven of these genes are known or likely to function in processes contributing to MHC-mediated antigen presentation. The remaining two are of unknown function. CIITA is thus uniquely dedicated for genes implicated in antigen presentation. The finding that CIITA regulates such a highly focused gene expression module sets it apart from all other transcription factors, for which large-scale binding-site mapping has indicated that they exert pleiotropic functions and regulate large numbers of genes