277 research outputs found
Multi-reggeon compound states and resummed anomalous dimensions in QCD
We perform the OPE analysis of the contribution of colour-singlet compound
states of reggeized gluons to a generic hard process in QCD and calculate the
spectrum of the corresponding higher twist anomalous dimensions in multi-colour
limit. These states govern high energy asymptotics of the structure functions
and their energies define the intercept of the Regge singularities both in the
Pomeron and the Odderon sectors. We argue that due to nontrivial analytical
properties of the energy spectrum, the twist expansion does not hold for the
gluonic states with the minimal energy generating the leading Regge
singularities. It is restored however after one takes into account the states
with larger energies whose contribution to the Regge asymptotics is subleading.Comment: 15 pages, 2 figures. Minor changes, references adde
Principles of statistical mechanics of random networks
We develop a statistical mechanics approach for random networks with
uncorrelated vertices. We construct equilibrium statistical ensembles of such
networks and obtain their partition functions and main characteristics. We find
simple dynamical construction procedures that produce equilibrium uncorrelated
random graphs with an arbitrary degree distribution. In particular, we show
that in equilibrium uncorrelated networks, fat-tailed degree distributions may
exist only starting from some critical average number of connections of a
vertex, in a phase with a condensate of edges.Comment: 14 pages, an extended versio
On the topological classification of binary trees using the Horton-Strahler index
The Horton-Strahler (HS) index has been shown to
be relevant to a number of physical (such at diffusion limited aggregation)
geological (river networks), biological (pulmonary arteries, blood vessels,
various species of trees) and computational (use of registers) applications.
Here we revisit the enumeration problem of the HS index on the rooted,
unlabeled, plane binary set of trees, and enumerate the same index on the
ambilateral set of rooted, plane binary set of trees of leaves. The
ambilateral set is a set of trees whose elements cannot be obtained from each
other via an arbitrary number of reflections with respect to vertical axes
passing through any of the nodes on the tree. For the unlabeled set we give an
alternate derivation to the existing exact solution. Extending this technique
for the ambilateral set, which is described by an infinite series of non-linear
functional equations, we are able to give a double-exponentially converging
approximant to the generating functions in a neighborhood of their convergence
circle, and derive an explicit asymptotic form for the number of such trees.Comment: 14 pages, 7 embedded postscript figures, some minor changes and typos
correcte
(Borel) convergence of the variationally improved mass expansion and the O(N) Gross-Neveu model mass gap
We reconsider in some detail a construction allowing (Borel) convergence of
an alternative perturbative expansion, for specific physical quantities of
asymptotically free models. The usual perturbative expansions (with an explicit
mass dependence) are transmuted into expansions in 1/F, where
for while for m \lsim \Lambda,
being the basic scale and given by renormalization group
coefficients. (Borel) convergence holds in a range of which corresponds to
reach unambiguously the strong coupling infrared regime near , which
can define certain "non-perturbative" quantities, such as the mass gap, from a
resummation of this alternative expansion. Convergence properties can be
further improved, when combined with expansion (variationally improved
perturbation) methods. We illustrate these results by re-evaluating, from
purely perturbative informations, the O(N) Gross-Neveu model mass gap, known
for arbitrary from exact S matrix results. Comparing different levels of
approximations that can be defined within our framework, we find reasonable
agreement with the exact result.Comment: 33 pp., RevTeX4, 6 eps figures. Minor typos, notation and wording
corrections, 2 references added. To appear in Phys. Rev.
Nucleon axial and pseudoscalar form factors from the covariant Faddeev equation
We compute the axial and pseudoscalar form factors of the nucleon in the
Dyson-Schwinger approach. To this end, we solve a covariant three-body Faddeev
equation for the nucleon wave function and determine the matrix elements of the
axialvector and pseudoscalar isotriplet currents. Our only input is a
well-established and phenomenologically successful ansatz for the
nonperturbative quark-gluon interaction. As a consequence of the axial
Ward-Takahashi identity that is respected at the quark level, the
Goldberger-Treiman relation is reproduced for all current-quark masses. We
discuss the timelike pole structure of the quark-antiquark vertices that enters
the nucleon matrix elements and determines the momentum dependence of the form
factors. Our result for the axial charge underestimates the experimental value
by 20-25% which might be a signal of missing pion-cloud contributions. The
axial and pseudoscalar form factors agree with phenomenological and lattice
data in the momentum range above Q^2 ~ 1...2 GeV^2.Comment: 17 pages, 7 figures, 1 tabl
Multiple Front Propagation Into Unstable States
The dynamics of transient patterns formed by front propagation in extended
nonequilibrium systems is considered. Under certain circumstances, the state
left behind a front propagating into an unstable homogeneous state can be an
unstable periodic pattern. It is found by a numerical solution of a model of
the Fr\'eedericksz transition in nematic liquid crystals that the mechanism of
decay of such periodic unstable states is the propagation of a second front
which replaces the unstable pattern by a another unstable periodic state with
larger wavelength. The speed of this second front and the periodicity of the
new state are analytically calculated with a generalization of the marginal
stability formalism suited to the study of front propagation into periodic
unstable states. PACS: 47.20.Ky, 03.40.Kf, 47.54.+rComment: 12 page
Fermat-linked relations for the Boubaker polynomial sequences via Riordan matrices analysis
The Boubaker polynomials are investigated in this paper. Using Riordan
matrices analysis, a sequence of relations outlining the relations with
Chebyshev and Fermat polynomials have been obtained. The obtained expressions
are a meaningful supply to recent applied physics studies using the Boubaker
polynomials expansion scheme (BPES).Comment: 12 pages, LaTe
Self-Similar Factor Approximants
The problem of reconstructing functions from their asymptotic expansions in
powers of a small variable is addressed by deriving a novel type of
approximants. The derivation is based on the self-similar approximation theory,
which presents the passage from one approximant to another as the motion
realized by a dynamical system with the property of group self-similarity. The
derived approximants, because of their form, are named the self-similar factor
approximants. These complement the obtained earlier self-similar exponential
approximants and self-similar root approximants. The specific feature of the
self-similar factor approximants is that their control functions, providing
convergence of the computational algorithm, are completely defined from the
accuracy-through-order conditions. These approximants contain the Pade
approximants as a particular case, and in some limit they can be reduced to the
self-similar exponential approximants previously introduced by two of us. It is
proved that the self-similar factor approximants are able to reproduce exactly
a wide class of functions which include a variety of transcendental functions.
For other functions, not pertaining to this exactly reproducible class, the
factor approximants provide very accurate approximations, whose accuracy
surpasses significantly that of the most accurate Pade approximants. This is
illustrated by a number of examples showing the generality and accuracy of the
factor approximants even when conventional techniques meet serious
difficulties.Comment: 22 pages + 11 ps figure
Schwinger-Dyson approach to non-equilibrium classical field theory
In this paper we discuss a Schwinger-Dyson [SD] approach for determining the
time evolution of the unequal time correlation functions of a non-equilibrium
classical field theory, where the classical system is described by an initial
density matrix at time . We focus on field theory in 1+1
space time dimensions where we can perform exact numerical simulations by
sampling an ensemble of initial conditions specified by the initial density
matrix. We discuss two approaches. The first, the bare vertex approximation
[BVA], is based on ignoring vertex corrections to the SD equations in the
auxiliary field formalism relevant for 1/N expansions. The second approximation
is a related approximation made to the SD equations of the original formulation
in terms of alone. We compare these SD approximations as well as a
Hartree approximation with exact numerical simulations. We find that both
approximations based on the SD equations yield good agreement with exact
numerical simulations and cure the late time oscillation problem of the Hartree
approximation. We also discuss the relationship between the quantum and
classical SD equations.Comment: 36 pages, 5 figure
Dependence of Variational Perturbation Expansions on Strong-Coupling Behavior. Inapplicability of delta-Expansion to Field Theory
We show that in applications of variational theory to quantum field theory it
is essential to account for the correct Wegner exponent omega governing the
approach to the strong-coupling, or scaling limit. Otherwise the procedure
either does not converge at all or to the wrong limit. This invalidates all
papers applying the so-called delta-expansion to quantum field theory.Comment: Author Information under
http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of
paper (including all PS fonts) at
http://www.physik.fu-berlin.de/~kleinert/34
- …