Quasi-exact solvability of Dirac equation with Lorentz scalar potential

We consider exact/quasi-exact solvability of Dirac equation with a Lorentz scalar potential based on factorizability of the equation. Exactly solvable and $sl(2)$-based quasi-exactly solvable potentials are discussed separately in Cartesian coordinates for a pure Lorentz potential depending only on one spatial dimension, and in spherical coordinates in the presence of a Dirac monopole.Comment: 10 pages, no figure

Higher Dimensional Geometries from Matrix Brane constructions

Matrix descriptions of even dimensional fuzzy spherical branes $S^{2k}$ in Matrix Theory and other contexts in Type II superstring theory reveal, in the large $N$ limit, higher dimensional geometries $SO(2k+1)/U(k)$, which have an interesting spectrum of $SO(2k+1)$ harmonics and can be up to 20 dimensional, while the spheres are restricted to be of dimension less than 10. In the case $k=2$, the matrix description has two dual field theory formulations. One involves a field theory living on the non-commutative coset $SO(5)/U(2)$ which is a fuzzy $S^2$ fibre bundle over a fuzzy $S^4$. In the other, there is a U(n) gauge theory on a fuzzy $S^4$ with ${\cal O}(n^3)$ instantons. The two descriptions can be related by exploiting the usual relation between the fuzzy two-sphere and U(n) Lie algebra. We discuss the analogous phenomena in the higher dimensional cases, developing a relation between fuzzy $SO(2k)/U(k)$ cosets and unitary Lie algebras.Comment: 28 pages (Harvmac big) ; version 2 : minor typos fixed and ref. adde

D0-branes in an H-field Background and Noncommutative Geometry

It is known that if we compactify D0-branes on a torus with constant B-field, the resulting theory becomes SYM theory on a noncommutative dual torus. We discuss the extension to the case of a H-field background. In the case of constant H-field on a three-torus, we derive the constraints to realize this compactification by considering the correspondence to string theory. We carry out this work as a first step to examine the possibility to describe transverse M5-branes in Matrix theory.Comment: 15 pages, LaTeX; some comments added, typos corrected, to appear in Nucl. Phys.

The vertical metal insulator semiconductor tunnel transistor: A proposed Fowler-Nordheim tunneling device

We propose a new field-effect transistor, the vertical metal insulator semiconductor tunnel transistor (VMISTT) which operates using gate modulation of the Fowler-Nordheim tunneling current through a metal insulator semiconductor (M-I-S) diode. The VMISTT has significant advantages over the metal-oxide-semiconductor field-effect transistor in device scaling. In order to allow room-temperature operation of the VMISTT, the tunnel oxide has to be optimized for the metal-to-insulator barrier height and the current-voltage characteristics. We have grown TiO2 layers as the tunnel insulator by oxidizing 7 and 10 nm thick Ti metal films vacuum-evaporated on silicon substrates, and characterized the films by current-voltage and capacitance-voltage techniques. The quality of the oxide films showed variations, depending on the oxidation temperatures in the range of 450-550 degrees C. Fowler-Nordheim tunneling was observed at low temperatures at bias voltage of 2 V and above and a barrier height of approximately 0.4 eV was calculated. Leakage currents present were due Schottky-barrier emission at room-temperature, and hopping at liquid nitrogen temperature

Optimal Photon Generation from Spontaneous Raman Processes in Cold Atoms

Spontaneous Raman processes in cold atoms have been widely used in the past decade for generating single photons. Here, we present a method to optimize their efficiencies for given atomic coherences and optical depths. We give a simple and complete recipe that can be used in present-day experiments, attaining near-optimal single photon emission while preserving the photon purity.Comment: 6+6 pages, 3 figures, 1 tabl

Financing Direct Democracy: Revisiting the Research on Campaign Spending and Citizen Initiatives

The conventional view in the direct democracy literature is that spending against a measure is more effective than spending in favor of a measure, but the empirical results underlying this conclusion have been questioned by recent research. We argue that the conventional finding is driven by the endogenous nature of campaign spending: initiative proponents spend more when their ballot measure is likely to fail. We address this endogeneity by using an instrumental variables approach to analyze a comprehensive dataset of ballot propositions in California from 1976 to 2004. We find that both support and opposition spending on citizen initiatives have strong, statistically significant, and countervailing effects. We confirm this finding by looking at time series data from early polling on a subset of these measures. Both analyses show that spending in favor of citizen initiatives substantially increases their chances of passage, just as opposition spending decreases this likelihood

A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems

Prethermalization refers to the transient phenomenon where a system thermalizes according to a Hamiltonian that is not the generator of its evolution. We provide here a rigorous framework for quantum spin systems where prethermalization is exhibited for very long times. First, we consider quantum spin systems under periodic driving at high frequency $\nu$. We prove that up to a quasi-exponential time $\tau_* \sim e^{c \frac{\nu}{\log^3 \nu}}$, the system barely absorbs energy. Instead, there is an effective local Hamiltonian $\hat D$ that governs the time evolution up to $\tau_*$, and hence this effective Hamiltonian is a conserved quantity up to $\tau_*$. Next, we consider systems without driving, but with a separation of energy scales in the Hamiltonian. A prime example is the Fermi-Hubbard model where the interaction $U$ is much larger than the hopping $J$. Also here we prove the emergence of an effective conserved quantity, different from the Hamiltonian, up to a time $\tau_*$ that is (almost) exponential in $U/J$.Comment: 21 pages, file updated to match published versio