13,377 research outputs found
The Phase Diagram and Spectrum of Gauge-Fixed Abelian Lattice Gauge Theory
We consider a lattice discretization of a covariantly gauge-fixed abelian
gauge theory. The gauge fixing is part of the action defining the theory, and
we study the phase diagram in detail. As there is no BRST symmetry on the
lattice, counterterms are needed, and we construct those explicitly. We show
that the proper adjustment of these counterterms drives the theory to a new
type of phase transition, at which we recover a continuum theory of (free)
photons. We present both numerical and (one-loop) perturbative results, and
show that they are in good agreement near this phase transition. Since
perturbation theory plays an important role, it is important to choose a
discretization of the gauge-fixing action such that lattice perturbation theory
is valid. Indeed, we find numerical evidence that lattice actions not
satisfying this requirement do not lead to the desired continuum limit. While
we do not consider fermions here, we argue that our results, in combination
with previous work, provide very strong evidence that this new phase transition
can be used to define abelian lattice chiral gauge theories.Comment: 42 pages, 30 figure
Shocks in unmagnetized plasma with a shear flow: Stability and magnetic field generation
A pair of curved shocks in a collisionless plasma is examined with a
two-dimensional particle-in-cell (PIC) simulation. The shocks are created by
the collision of two electron-ion clouds at a speed that exceeds everywhere the
threshold speed for shock formation. A variation of the collision speed along
the initially planar collision boundary, which is comparable to the ion
acoustic speed, yields a curvature of the shock that increases with time. The
spatially varying Mach number of the shocks results in a variation of the
downstream density in the direction along the shock boundary. This variation is
eventually equilibrated by the thermal diffusion of ions. The pair of shocks is
stable for tens of inverse ion plasma frequencies. The angle between the mean
flow velocity vector of the inflowing upstream plasma and the shock's
electrostatic field increases steadily during this time. The disalignment of
both vectors gives rise to a rotational electron flow, which yields the growth
of magnetic field patches that are coherent over tens of electron skin depths.Comment: 10 pages, 10 figures accepted for publication in Physics of Plasma
An \emph{ab initio} method for locating characteristic potential energy minima of liquids
It is possible in principle to probe the many--atom potential surface using
density functional theory (DFT). This will allow us to apply DFT to the
Hamiltonian formulation of atomic motion in monatomic liquids [\textit{Phys.
Rev. E} {\bf 56}, 4179 (1997)]. For a monatomic system, analysis of the
potential surface is facilitated by the random and symmetric classification of
potential energy valleys. Since the random valleys are numerically dominant and
uniform in their macroscopic potential properties, only a few quenches are
necessary to establish these properties. Here we describe an efficient
technique for doing this. Quenches are done from easily generated "stochastic"
configurations, in which the nuclei are distributed uniformly within a
constraint limiting the closeness of approach. For metallic Na with atomic pair
potential interactions, it is shown that quenches from stochastic
configurations and quenches from equilibrium liquid Molecular Dynamics (MD)
configurations produce statistically identical distributions of the structural
potential energy. Again for metallic Na, it is shown that DFT quenches from
stochastic configurations provide the parameters which calibrate the
Hamiltonian. A statistical mechanical analysis shows how the underlying
potential properties can be extracted from the distributions found in quenches
from stochastic configurations
Search for the disappearance of muon antineutrinos in the NuMI neutrino beam
We report constraints on muon antineutrino oscillation parameters that were obtained by using the two MINOS detectors to measure the 7% antineutrino component of the NuMI neutrino beam. In the Far Detector, we select 130 events in the charged-current muon antineutrino sample, compared to a prediction of 136.4 +/- 11.7(stat) ^{+10.2}_{-8.9}(syst) events under the assumption |dm2bar|=2.32x10^-3 eV^2, snthetabar=1.0. A fit to the two-flavor oscillation approximation constrains |dm2bar|<3.37x10^-3 eV^2 at the 90% confidence level with snthetabar=1.0
Optical Conductivity in a Two-Band Superconductor: Pb
We demonstrate the effect of bandstructure on the superconducting properties
of Pb by calculating the strong-coupling features in the optical conductivity,
, due to the electron-phonon interaction. The importance of
momentum dependence in the calculation of the properties of superconductors has
previously been raised for MgB. Pb resembles MgB in that it is a two
band superconductor in which the bands' contributions to the Fermi surface have
very different topologies. We calculate by calculating a
memory function which has been recently used to analyze of
BiSrCaCuO. In our calculations the two components of
the Fermi surface are described by parameterizations of de Haas--van Alphen
data. We use a phonon spectrum which is a fit to neutron scattering data. By
including the momentum dependence of the Fermi surface good agreement is found
with the experimentally determined strong-coupling features which can be
described by a broad peak at around 4.5 meV and a narrower higher peak around 8
meV of equal height. The calculated features are found to be dominated by
scattering between states within the third band. By contrast scattering between
states in the second band leads to strong-coupling features in which the height
of the high energy peak is reduced by compared to that of the low
energy peak. This result is similar to that in the conventional isotropic
(momentum independent) treatment of superconductivity. Our results show that it
is important to use realistic models of the bandstructure and phonons, and to
avoid using momentum averaged quantities, in calculations in order to get
quantitatively accurate results
Chiral Fermions on the Lattice through Gauge Fixing -- Perturbation Theory
We study the gauge-fixing approach to the construction of lattice chiral
gauge theories in one-loop weak-coupling perturbation theory. We show how
infrared properties of the gauge degrees of freedom determine the nature of the
continuous phase transition at which we take the continuum limit. The fermion
self-energy and the vacuum polarization are calculated, and confirm that, in
the abelian case, this approach can be used to put chiral gauge theories on the
lattice in four dimensions. We comment on the generalization to the nonabelian
case.Comment: 31 pages, 5 figures, two refs. adde
Computing Inferences for Large-Scale Continuous-Time Markov Chains by Combining Lumping with Imprecision
If the state space of a homogeneous continuous-time Markov chain is too
large, making inferences - here limited to determining marginal or limit
expectations - becomes computationally infeasible. Fortunately, the state space
of such a chain is usually too detailed for the inferences we are interested
in, in the sense that a less detailed - smaller - state space suffices to
unambiguously formalise the inference. However, in general this so-called
lumped state space inhibits computing exact inferences because the
corresponding dynamics are unknown and/or intractable to obtain. We address
this issue by considering an imprecise continuous-time Markov chain. In this
way, we are able to provide guaranteed lower and upper bounds for the
inferences of interest, without suffering from the curse of dimensionality.Comment: 9th International Conference on Soft Methods in Probability and
Statistics (SMPS 2018
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