G0^0 Electronics and Data Acquisition (Forward-Angle Measurements)

The G$^0$ parity-violation experiment at Jefferson Lab (Newport News, VA) is designed to determine the contribution of strange/anti-strange quark pairs to the intrinsic properties of the proton. In the forward-angle part of the experiment, the asymmetry in the cross section was measured for $\vec{e}p$ elastic scattering by counting the recoil protons corresponding to the two beam-helicity states. Due to the high accuracy required on the asymmetry, the G$^0$ experiment was based on a custom experimental setup with its own associated electronics and data acquisition (DAQ) system. Highly specialized time-encoding electronics provided time-of-flight spectra for each detector for each helicity state. More conventional electronics was used for monitoring (mainly FastBus). The time-encoding electronics and the DAQ system have been designed to handle events at a mean rate of 2 MHz per detector with low deadtime and to minimize helicity-correlated systematic errors. In this paper, we outline the general architecture and the main features of the electronics and the DAQ system dedicated to G$^0$ forward-angle measurements.Comment: 35 pages. 17 figures. This article is to be submitted to NIM section A. It has been written with Latex using \documentclass{elsart}. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment In Press (2007

Precise variational tunneling rates for anharmonic oscillator with g<0

We systematically improve the recent variational calculation of the imaginary part of the ground state energy of the quartic anharmonic oscillator. The results are extremely accurate as demonstrated by deriving, from the calculated imaginary part, all perturbation coefficients via a dispersion relation and reproducing the exact values with a relative error of less than $10^{-5}$. A comparison is also made with results of a Schr\"{o}dinger calculation based on the complex rotation method.Comment: PostScrip

Monte Carlo simulation of a hard-sphere gas in the planar Fourier flow with a gravity field

By means of the Direct Simulation Monte Carlo method, the Boltzmann equation is numerically solved for a gas of hard spheres enclosed between two parallel plates kept at different temperatures and subject to the action of a gravity field normal to the plates. The profiles of pressure, density, temperature and heat flux are seen to be quite sensitive to the value of the gravity acceleration $g$. If the gravity field and the heat flux are parallel ($g>0$), the magnitudes of both the temperature gradient and the heat flux are smaller than in the opposite case ($g<0$). When considering the actual heat flux relative to the value predicted by the Fourier law, it is seen that, if $g>0$, the ratio increases as the reduced local field strength increases, while the opposite happens if $g<0$. The simulation results are compared with theoretical predictions for Maxwell moleculesComment: 18 pages (LaTex), 7 figures (eps

Finite vs infinite decompositions in conformal embeddings

Building on work of the first and last author, we prove that an embedding of simple affine vertex algebras $V_{\mathbf{k}}(\mathfrak g^0)\subset V_{k}(\mathfrak g)$, corresponding to an embedding of a maximal equal rank reductive subalgebra $\mathfrak g^0$ into a simple Lie algebra $\mathfrak g$, is conformal if and only if the corresponding central charges are equal. We classify the equal rank conformal embeddings. Furthermore we describe, in almost all cases, when $V_{k}(\mathfrak g)$ decomposes finitely as a $V_{\mathbf{k}}(\mathfrak g^0)$-module.Comment: Latex file, 31 pages, minor corrections, to appear in Communications in Mathematical Physic

Lower Spectral Branches of a Particle Coupled to a Bose Field

The structure of the lower part (i.e. $\epsilon$-away below the two-boson threshold) spectrum of Fr\"ohlich's polaron Hamiltonian in the weak coupling regime is obtained in spatial dimension $d\geq 3$. It contains a single polaron branch defined for total momentum $p\in G^{(0)}$, where $G^{(0)}\subset {\mathbb R}^d$ is a bounded domain, and, for any $p\in {\mathbb R}^d$, a manifold of polaron + one-boson states with boson momentum $q$ in a bounded domain depending on $p$. The polaron becomes unstable and dissolves into the one boson manifold at the boundary of $G^{(0)}$. The dispersion laws and generalized eigenfunctions are calculated