18,732 research outputs found
The Dimensional Recurrence and Analyticity Method for Multicomponent Master Integrals: Using Unitarity Cuts to Construct Homogeneous Solutions
We consider the application of the DRA method to the case of several master
integrals in a given sector. We establish a connection between the homogeneous
part of dimensional recurrence and maximal unitarity cuts of the corresponding
integrals: a maximally cut master integral appears to be a solution of the
homogeneous part of the dimensional recurrence relation. This observation
allows us to make a necessary step of the DRA method, the construction of the
general solution of the homogeneous equation, which, in this case, is a coupled
system of difference equations.Comment: 17 pages, 2 figure
Two-Loop Iteration of Five-Point N=4 Super-Yang-Mills Amplitudes
We confirm by explicit computation the conjectured all-orders iteration of
planar maximally supersymmetric N=4 Yang-Mills theory in the nontrivial case of
five-point two-loop amplitudes. We compute the required unitarity cuts of the
integrand and evaluate the resulting integrals numerically using a
Mellin--Barnes representation and the automated package of ref.~[1]. This
confirmation of the iteration relation provides further evidence suggesting
that N=4 gauge theory is solvable.Comment: 4 pages, 3 figure
On a general analytical formula for U_q(su(3))-Clebsch-Gordan coefficients
We present the projection operator method in combination with the
Wigner-Racah calculus of the subalgebra U_q(su(2)) for calculation of
Clebsch-Gordan coefficients (CGCs) of the quantum algebra U_q(su(3)). The key
formulas of the method are couplings of the tensor and projection operators and
also a tensor form for the projection operator of U_q(su(3)). We obtain a very
compact general analytical formula for the U_q(su(3)) CGCs in terms of the
U_q(su(2)) Wigner 3nj-symbols.Comment: 9 pages, LaTeX; to be published in Yad. Fiz. (Phys. Atomic Nuclei),
(2001
Aspherical PIC code (APIC) for modeling non-spherical dust in plasmas using shape-conforming coordinates
The 2D3V Aspherical Particle-in-Cell (APIC) code is developed for modeling of
interactions of non-spherical dust grains with plasmas. It simulates the motion
of plasma electrons and ions in a self-consistent electric field of
plasma-screened charged dust particle. Due to absorption/recombination of
plasma particles impinging on the grain surface, they transfer charge,
momentum, angular momentum, as well as kinetic and binding energy, creating
currents, forces, torques, and heat fluxes to the grain. The values of such
physical parameters determine dust behavior in plasma, including its dynamics
and ablation, and can be used in various plasma studies and applications, such
as dusty plasmas, fusion devices, laboratory experiments, and astrophysical
research. Obtaining these physical values for select non-spherical shapes of
conducting dust grains is the main goal of the APIC code simulations
Conformal Curves in Potts Model: Numerical Calculation
We calculated numerically the fractal dimension of the boundaries of the
Fortuin-Kasteleyn clusters of the -state Potts model for integer and
non-integer values of on the square lattice.
In addition we calculated with high accuracy the fractal dimension of the
boundary points of the same clusters on the square domain. Our calculation
confirms that this curves can be described by SLE.Comment: 11 Pages, 4 figure
Computing the Loewner driving process of random curves in the half plane
We simulate several models of random curves in the half plane and numerically
compute their stochastic driving process (as given by the Loewner equation).
Our models include models whose scaling limit is the Schramm-Loewner evolution
(SLE) and models for which it is not. We study several tests of whether the
driving process is Brownian motion. We find that just testing the normality of
the process at a fixed time is not effective at determining if the process is
Brownian motion. Tests that involve the independence of the increments of
Brownian motion are much more effective. We also study the zipper algorithm for
numerically computing the driving function of a simple curve. We give an
implementation of this algorithm which runs in a time O(N^1.35) rather than the
usual O(N^2), where N is the number of points on the curve.Comment: 20 pages, 4 figures. Changes to second version: added new paragraph
to conclusion section; improved figures cosmeticall
Four-dimensional integration by parts with differential renormalization as a method of evaluation of Feynman diagrams
It is shown how strictly four-dimensional integration by parts combined with
differential renormalization and its infrared analogue can be applied for
calculation of Feynman diagrams.Comment: 6 pages, late
Analysis of a fully packed loop model arising in a magnetic Coulomb phase
The Coulomb phase of spin ice, and indeed the Ic phase of water ice,
naturally realise a fully-packed two-colour loop model in three dimensions. We
present a detailed analysis of the statistics of these loops, which avoid
themselves and other loops of the same colour, and contrast their behaviour to
an analogous two-dimensional model. The properties of another extended degree
of freedom are also addressed, flux lines of the emergent gauge field of the
Coulomb phase, which appear as "Dirac strings" in spin ice. We mention
implications of these results for related models, and experiments.Comment: 5 pages, 4 figure
- …