97 research outputs found
Entropy and the variational principle for actions of sofic groups
Recently Lewis Bowen introduced a notion of entropy for measure-preserving
actions of a countable sofic group on a standard probability space admitting a
generating partition with finite entropy. By applying an operator algebra
perspective we develop a more general approach to sofic entropy which produces
both measure and topological dynamical invariants, and we establish the
variational principle in this context. In the case of residually finite groups
we use the variational principle to compute the topological entropy of
principal algebraic actions whose defining group ring element is invertible in
the full group C*-algebra.Comment: 44 pages; minor changes; to appear in Invent. Mat
On Motives Associated to Graph Polynomials
The appearance of multiple zeta values in anomalous dimensions and
-functions of renormalizable quantum field theories has given evidence
towards a motivic interpretation of these renormalization group functions. In
this paper we start to hunt the motive, restricting our attention to a subclass
of graphs in four dimensional scalar field theory which give scheme independent
contributions to the above functions.Comment: 54
Novel approaches to the construction of miniaturized analytical instrumentation
This paper focuses on the design, construction, preliminary testing, and potential applications of three forms of miniaturized analytical instrumentation. The first is an optical fiber instrument for monitoring pH and other cations in aqueous solutions. The instrument couples chemically selective indicators that were immobilized at porous polymeric films with a hardware package that provides the excitation light source, required optical components, and detection and data processing hardware. The second is a new form of a piezoelectric mass sensor. The sensor was fabricated by the deposition of a thin (5.5 micron) film of piezoelectric aluminum nitride (AIN). The completed deposition process yields a thin film resonator (TFR) that is shaped as a 400 micron square and supports a standing bulk acoustic wave in a longitudinal mode at frequencies of approx. 1 GHz. Various deposition and vapor sorption studies indicate that the mass sensitivity of the TFR's rival those of the most sensitive mass sensors currently available, though offering such performance in a markedly smaller device. The third couples a novel form of liquid chromatography with microlithographic miniaturization techniques. The status of the miniaturization effort, the goal of which is to achieve chip-scale separations, is briefly discussed
Phase diagram and critical properties in the Polyakov--Nambu--Jona-Lasinio model
We investigate the phase diagram of the so-called
Polyakov--Nambu--Jona-Lasinio model at finite temperature and nonzero chemical
potential with three quark flavours. Chiral and deconfinement phase transitions
are discussed, and the relevant order-like parameters are analyzed. The results
are compared with simple thermodynamic expectations and lattice data. A special
attention is payed to the critical end point: as the strength of the
flavour-mixing interaction becomes weaker, the critical end point moves to low
temperatures and can even disappear.Comment: Talk given at the 9th International Conference on Quark Confinement
and the Hadron Spectrum - QCHS IX, Madrid, Spain, 30 August - September 201
Search for Lorentz and CPT Violation Effects in Muon Spin Precession
The spin precession frequency of muons stored in the storage ring has
been analyzed for evidence of Lorentz and CPT violation. Two Lorentz and CPT
violation signatures were searched for: a nonzero
(=); and a sidereal variation of
. No significant effect is found, and the following
limits on the standard-model extension parameters are obtained: GeV; GeV; and the 95% confidence level limits
GeV and
GeV.Comment: 5 pages, 3 figures, submitted to Physical Review Letters, Modified to
answer the referees suggestion
An Improved Limit on the Muon Electric Dipole Moment
Three independent searches for an electric dipole moment (EDM) of the
positive and negative muons have been performed, using spin precession data
from the muon g-2 storage ring at Brookhaven National Laboratory. Details on
the experimental apparatus and the three analyses are presented. Since the
individual results on the positive and negative muon, as well as the combined
result, d=-0.1(0.9)E-19 e-cm, are all consistent with zero, we set a new muon
EDM limit, |d| < 1.9E-19 e-cm (95% C.L.). This represents a factor of 5
improvement over the previous best limit on the muon EDM.Comment: 19 pages, 15 figures, 7 table
News from the Muon (g-2) Experiment at BNL
The magnetic moment anomaly a_mu = (g_mu - 2) / 2 of the positive muon has
been measured at the Brookhaven Alternating Gradient Synchrotron with an
uncertainty of 0.7 ppm. The new result, based on data taken in 2000, agrees
well with previous measurements. Standard Model evaluations currently differ
from the experimental result by 1.6 to 3.0 standard deviations.Comment: Talk presented at RADCOR - Loops and Legs 2002, Kloster Banz,
Germany, September 8-13 2002, to be published in Nuclear Physics B (Proc.
Suppl.); 5 pages, 3 figure
Final Report of the Muon E821 Anomalous Magnetic Moment Measurement at BNL
We present the final report from a series of precision measurements of the
muon anomalous magnetic moment, a_mu = (g-2)/2. The details of the experimental
method, apparatus, data taking, and analysis are summarized. Data obtained at
Brookhaven National Laboratory, using nearly equal samples of positive and
negative muons, were used to deduce a_mu(Expt) = 11 659 208.0(5.4)(3.3) x
10^-10, where the statistical and systematic uncertainties are given,
respectively. The combined uncertainty of 0.54 ppm represents a 14-fold
improvement compared to previous measurements at CERN. The standard model value
for a_mu includes contributions from virtual QED, weak, and hadronic processes.
While the QED processes account for most of the anomaly, the largest
theoretical uncertainty, ~0.55 ppm, is associated with first-order hadronic
vacuum polarization. Present standard model evaluations, based on e+e- hadronic
cross sections, lie 2.2 - 2.7 standard deviations below the experimental
result.Comment: Summary paper of E821 Collaboration measurements of the muon
anomalous magnetic moment, each reported earlier in Letters or Brief Reports;
96 pages, 41 figures, 16 tables. Revised version submitted to PR
Search for Lorentz and CPT Violation Effects in Muon Spin Precession
The spin precession frequency of muons stored in the storage ring has
been analyzed for evidence of Lorentz and CPT violation. Two Lorentz and CPT
violation signatures were searched for: a nonzero
(=); and a sidereal variation of
. No significant effect is found, and the following
limits on the standard-model extension parameters are obtained: GeV; GeV; and the 95% confidence level limits
GeV and
GeV.Comment: 5 pages, 3 figures, submitted to Physical Review Letters, Modified to
answer the referees suggestion
Three-variable Mahler measures and special values of modular and Dirichlet -series
In this paper we prove that the Mahler measures of the Laurent polynomials
, ,
and , for various values of , are of the form , where , is a CM newform of
weight 3, and is a quadratic character. Since it has been proved that
these Maher measures can also be expressed in terms of logarithms and
-hypergeometric series, we obtain several new hypergeometric evaluations
and transformations from these results
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