318 research outputs found
Random walks on combs
We develop techniques to obtain rigorous bounds on the behaviour of random
walks on combs. Using these bounds we calculate exactly the spectral dimension
of random combs with infinite teeth at random positions or teeth with random
but finite length. We also calculate exactly the spectral dimension of some
fixed non-translationally invariant combs. We relate the spectral dimension to
the critical exponent of the mass of the two-point function for random walks on
random combs, and compute mean displacements as a function of walk duration. We
prove that the mean first passage time is generally infinite for combs with
anomalous spectral dimension.Comment: 42 pages, 4 figure
Two-band random matrices
Spectral correlations in unitary invariant, non-Gaussian ensembles of large
random matrices possessing an eigenvalue gap are studied within the framework
of the orthogonal polynomial technique. Both local and global characteristics
of spectra are directly reconstructed from the recurrence equation for
orthogonal polynomials associated with a given random matrix ensemble. It is
established that an eigenvalue gap does not affect the local eigenvalue
correlations which follow the universal sine and the universal multicritical
laws in the bulk and soft-edge scaling limits, respectively. By contrast,
global smoothed eigenvalue correlations do reflect the presence of a gap, and
are shown to satisfy a new universal law exhibiting a sharp dependence on the
odd/even dimension of random matrices whose spectra are bounded. In the case of
unbounded spectrum, the corresponding universal `density-density' correlator is
conjectured to be generic for chaotic systems with a forbidden gap and broken
time reversal symmetry.Comment: 12 pages (latex), references added, discussion enlarge
Quantum gravity and the standard model
We show that a class of background independent models of quantum spacetime
have local excitations that can be mapped to the first generation fermions of
the standard model of particle physics. These states propagate coherently as
they can be shown to be noiseless subsystems of the microscopic quantum
dynamics. These are identified in terms of certain patterns of braiding of
graphs, thus giving a quantum gravitational foundation for the topological
preon model proposed by one of us.
These results apply to a large class of theories in which the Hilbert space
has a basis of states given by ribbon graphs embedded in a three-dimensional
manifold up to diffeomorphisms, and the dynamics is given by local moves on the
graphs, such as arise in the representation theory of quantum groups. For such
models, matter appears to be already included in the microscopic kinematics and
dynamics.Comment: 12 pages, 21 figures, improved presentation, results unchange
A discrete, unitary, causal theory of quantum gravity
A discrete model of Lorentzian quantum gravity is proposed. The theory is
completely background free, containing no reference to absolute space, time, or
simultaneity. The states at one slice of time are networks in which each vertex
is labelled with two arrows, which point along an adjacent edge, or to the
vertex itself. The dynamics is specified by a set of unitary replacement rules,
which causally propagate the local degrees of freedom. The inner product
between any two states is given by a sum over histories. Assuming it converges
(or can be Abel resummed), this inner product is proven to be hermitian and
fully gauge-degenerate under spacetime diffeomorphisms. At least for states
with a finite past, the inner product is also positive. This allows a Hilbert
space of physical states to be constructed.Comment: 38 pages, 9 figures, v3 added to exposition and references, v4
expanded prospects sectio
Measurement of the Luminosity in the ZEUS Experiment at HERA II
The luminosity in the ZEUS detector was measured using photons from electron
bremsstrahlung. In 2001 the HERA collider was upgraded for operation at higher
luminosity. At the same time the luminosity-measuring system of the ZEUS
experiment was modified to tackle the expected higher photon rate and
synchrotron radiation. The existing lead-scintillator calorimeter was equipped
with radiation hard scintillator tiles and shielded against synchrotron
radiation. In addition, a magnetic spectrometer was installed to measure the
luminosity independently using photons converted in the beam-pipe exit window.
The redundancy provided a reliable and robust luminosity determination with a
systematic uncertainty of 1.7%. The experimental setup, the techniques used for
luminosity determination and the estimate of the systematic uncertainty are
reported.Comment: 25 pages, 11 figure
Spectra of massive and massless QCD Dirac operators: A novel link
We show that integrable structure of chiral random matrix models incorporating global symmetries of QCD Dirac operators (labeled by the Dyson index beta=1,2, and 4) leads to emergence of a connection relation between the spectral statistics of massive and massless Dirac operators. This novel link established for beta-fold degenerate massive fermions is used to explicitly derive (and prove the random matrix universality of) statistics of low--lying eigenvalues of QCD Dirac operators in the presence of SU(2) massive fermions in the fundamental representation (beta=1) and SU(N_c >= 2) massive adjoint fermions (beta=4). Comparison with available lattice data for SU(2) dynamical staggered fermions reveals a good agreement
"Single Ring Theorem" and the Disk-Annulus Phase Transition
Recently, an analytic method was developed to study in the large limit
non-hermitean random matrices that are drawn from a large class of circularly
symmetric non-Gaussian probability distributions, thus extending the existing
Gaussian non-hermitean literature. One obtains an explicit algebraic equation
for the integrated density of eigenvalues from which the Green's function and
averaged density of eigenvalues could be calculated in a simple manner. Thus,
that formalism may be thought of as the non-hermitean analog of the method due
to Br\'ezin, Itzykson, Parisi and Zuber for analyzing hermitean non-Gaussian
random matrices. A somewhat surprising result is the so called "Single Ring"
theorem, namely, that the domain of the eigenvalue distribution in the complex
plane is either a disk or an annulus. In this paper we extend previous results
and provide simple new explicit expressions for the radii of the eigenvalue
distiobution and for the value of the eigenvalue density at the edges of the
eigenvalue distribution of the non-hermitean matrix in terms of moments of the
eigenvalue distribution of the associated hermitean matrix. We then present
several numerical verifications of the previously obtained analytic results for
the quartic ensemble and its phase transition from a disk shaped eigenvalue
distribution to an annular distribution. Finally, we demonstrate numerically
the "Single Ring" theorem for the sextic potential, namely, the potential of
lowest degree for which the "Single Ring" theorem has non-trivial consequences.Comment: latex, 5 eps figures, 41 page
The distribution of pond snail communities across a landscape: separating out the influence of spatial position from local habitat quality for ponds in south-east Northumberland, UK
Ponds support a rich biodiversity because the heterogeneity of individual ponds creates, at the landscape scale, a diversity of habitats for wildlife. The distribution of pond animals and plants will be influenced by both the local conditions within a pond and the spatial distribution of ponds across the landscape. Separating out the local from the spatial is difficult because the two are often linked. Pond snails are likely to be affected by both local conditions, e.g. water hardness, and spatial patterns, e.g. distance between ponds, but studies of snail communities struggle distinguishing between the two. In this study, communities of snails were recorded from 52 ponds in a biogeographically coherent landscape in north-east England. The distribution of snail communities was compared to local environments characterised by the macrophyte communities within each pond and to the spatial pattern of ponds throughout the landscape. Mantel tests were used to partial out the local versus the landscape respective influences. Snail communities became more similar in ponds that were closer together and in ponds with similar macrophyte communities as both the local and the landscape scale were important for this group of animals. Data were collected from several types of ponds, including those created on nature reserves specifically for wildlife, old field ponds (at least 150 years old) primarily created for watering livestock and subsidence ponds outside protected areas or amongst coastal dunes. No one pond type supported all the species. Larger, deeper ponds on nature reserves had the highest numbers of species within individual ponds but shallow, temporary sites on farm land supported a distinct temporary water fauna. The conservation of pond snails in this region requires a diversity of pond types rather than one idealised type and ponds scattered throughout the area at a variety of sites, not just concentrated on nature reserves
On "Dotsenko-Fateev" representation of the toric conformal blocks
We demonstrate that the recent ansatz of arXiv:1009.5553, inspired by the
original remark due to R.Dijkgraaf and C.Vafa, reproduces the toric conformal
blocks in the same sense that the spherical blocks are given by the integral
representation of arXiv:1001.0563 with a peculiar choice of open integration
contours for screening insertions. In other words, we provide some evidence
that the toric conformal blocks are reproduced by appropriate beta-ensembles
not only in the large-N limit, but also at finite N. The check is explicitly
performed at the first two levels for the 1-point toric functions.
Generalizations to higher genera are briefly discussed.Comment: 10 page
Deconfining Phase Transition as a Matrix Model of Renormalized Polyakov Loops
We discuss how to extract renormalized from bare Polyakov loops in SU(N)
lattice gauge theories at nonzero temperature in four spacetime dimensions.
Single loops in an irreducible representation are multiplicatively renormalized
without mixing, through a renormalization constant which depends upon both
representation and temperature. The values of renormalized loops in the four
lowest representations of SU(3) were measured numerically on small, coarse
lattices. We find that in magnitude, condensates for the sextet and octet loops
are approximately the square of the triplet loop. This agrees with a large
expansion, where factorization implies that the expectation values of loops in
adjoint and higher representations are just powers of fundamental and
anti-fundamental loops. For three colors, numerically the corrections to the
large relations are greatest for the sextet loop, ; these
represent corrections of for N=3. The values of the renormalized
triplet loop can be described by an SU(3) matrix model, with an effective
action dominated by the triplet loop. In several ways, the deconfining phase
transition for N=3 appears to be like that in the matrix model of
Gross and Witten.Comment: 24 pages, 7 figures; v2, 27 pages, 12 figures, extended discussion
for clarity, results unchange
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