Generalized canonical ensembles and ensemble equivalence

This paper is a companion article to our previous paper (J. Stat. Phys. 119, 1283 (2005), cond-mat/0408681), which introduced a generalized canonical ensemble obtained by multiplying the usual Boltzmann weight factor $e^{-\beta H}$ of the canonical ensemble with an exponential factor involving a continuous function $g$ of the Hamiltonian $H$. We provide here a simplified introduction to our previous work, focusing now on a number of physical rather than mathematical aspects of the generalized canonical ensemble. The main result discussed is that, for suitable choices of $g$, the generalized canonical ensemble reproduces, in the thermodynamic limit, all the microcanonical equilibrium properties of the many-body system represented by $H$ even if this system has a nonconcave microcanonical entropy function. This is something that in general the standard ($g=0$) canonical ensemble cannot achieve. Thus a virtue of the generalized canonical ensemble is that it can be made equivalent to the microcanonical ensemble in cases where the canonical ensemble cannot. The case of quadratic $g$-functions is discussed in detail; it leads to the so-called Gaussian ensemble.Comment: 8 pages, 4 figures (best viewed in ps), revtex4. Changes in v2: Title changed, references updated, new paragraph added, minor differences with published versio

Determination of nuclear parton distribution functions and their uncertainties at next-to-leading order

Nuclear parton distribution functions (NPDFs) are determined by global analyses of experimental data on structure-function ratios F_2^A/F_2^{A'} and Drell-Yan cross-section ratios \sigma_{DY}^A/\sigma_{DY}^{A'}. The analyses are done in the leading order (LO) and next-to-leading order (NLO) of running coupling constant \alpha_s. Uncertainties of the NPDFs are estimated in both LO and NLO for finding possible NLO improvement. Valence-quark distributions are well determined, and antiquark distributions are also determined at x<0.1. However, the antiquark distributions have large uncertainties at x>0.2. Gluon modifications cannot be fixed at this stage. Although the advantage of the NLO analysis, in comparison with the LO one, is generally the sensitivity to the gluon distributions, gluon uncertainties are almost the same in the LO and NLO. It is because current scaling-violation data are not accurate enough to determine precise nuclear gluon distributions. Modifications of the PDFs in the deuteron are also discussed by including data on the proton-deuteron ratio F_2^D/F_2^p in the analysis. A code is provided for calculating the NPDFs and their uncertainties at given x and Q^2 in the LO and NLO.Comment: 15 pages, LaTeX, 22 eps files, to appear in PRC. A code for calculating our nuclear parton distribution functions and their uncertainties can be obtained from http://research.kek.jp/people/kumanos/nuclp.htm

Local freedom in the gravitational field

In a cosmological context, the electric and magnetic parts of the Weyl tensor, E_{ab} and H_{ab}, represent the locally free curvature - i.e. they are not pointwise determined by the matter fields. By performing a complete covariant decomposition of the derivatives of E_{ab} and H_{ab}, we show that the parts of the derivative of the curvature which are locally free (i.e. not pointwise determined by the matter via the Bianchi identities) are exactly the symmetrised trace-free spatial derivatives of E_{ab} and H_{ab} together with their spatial curls. These parts of the derivatives are shown to be crucial for the existence of gravitational waves.Comment: New results on gravitational waves included; new references added; revised version (IOP style) to appear Class. Quantum Gra

Terahertz dynamics of a topologically protected state: quantum Hall effect plateaus near cyclotron resonance in a GaAs/AlGaAs heterojunction

We measure the Hall conductivity of a two-dimensional electron gas formed at a GaAs/AlGaAs heterojunction in the terahertz regime close to the cyclotron resonance frequency by employing a highly sensitive Faraday rotation method coupled with electrical gating of the sample to change the electron density. We observe clear plateau-and step-like features in the Faraday rotation angle vs. electron density and magnetic field (Landau-level filling factor), which are the high frequency manifestation of quantum Hall plateaus - a signature of topologically protected edge states. The results are compared to a recent dynamical scaling theory.Comment: 18 pages, 3 figure

Radiation measurements from polar and geosynchronous satellites

The following topics are discussed: (1) cloud effects in climate determination; (2) annual variation in the global heat balance of the earth; (3) the accuracy of precipitation estimates made from passive microwave measurements from satellites; (4) seasonal oceanic precipitation frequencies; (5) determination of mesoscale temperature and moisture fields over land from satellite radiance measurements; and (6) Nimbus 6 scanning microwave spectrometer data evaluation for surface wind and pressure components in tropical storms

Observation of Asymmetric Transport in Structures with Active Nonlinearities

A mechanism for asymmetric transport based on the interplay between the fundamental symmetries of parity (P) and time (T) with nonlinearity is presented. We experimentally demonstrate and theoretically analyze the phenomenon using a pair of coupled van der Pol oscillators, as a reference system, one with anharmonic gain and the other with complementary anharmonic loss; connected to two transmission lines. An increase of the gain/loss strength or the number of PT-symmetric nonlinear dimers in a chain, can increase both the asymmetry and transmittance intensities.Comment: 5 pages, 5 figure

Jet Investigations Using the Radial Moment

We define the radial moment, , for jets produced in hadron-hadron collisions. It can be used as a tool for studying, as a function of the jet transverse energy and pseudorapidity, radiation within the jet and the quality of a perturbative description of the jet shape. We also discuss how non-perturbative corrections to the jet transverse energy affect .Comment: 14 pages, LaTeX, 6 figure