97,726 research outputs found
Summing One-Loop Graphs at Multi-Particle Threshold
It is shown that the technique recently suggested by Lowell Brown for summing
the tree graphs at threshold can be extended to calculate the loop effects.
Explicit result is derived for the sum of one-loop graphs for the amplitude of
threshold production of on-mass-shell particles by one virtual in the
unbroken theory. It is also found that the tree-level
amplitude of production of particles by two incoming on-mass-shell
particles vanishes at the threshold for .Comment: 13 pages, LaTeX, TPI-MINN-92/45-
Stationary Nonlinear Schr\"odinger Equation on Simplest Graphs: Boundary conditions and exact solutions
We treat the stationary (cubic) nonlinear Schr\"odinger equation (NSLE) on
simplest graphs. Formulation of the problem and exact analytical solutions of
NLSE are presented for star graphs consisting of three bonds. It is shown that
the method can be extended for the case of arbitrary number of bonds of star
graphs and for other simplest topologies such as tree and loop graphs. The case
of repulsive and attractive nonlinearities are treated separately
On the Glue Content in Heavy Quarkonia
Starting with two coupled Bethe-Salpeter equations for the quark-antiquark,
and for the quark-glue-antiquark component of the quarkonium, we solve the
bound state equations perturbatively. The resulting admixture of glue can be
partially understood in a semiclassical way, one has, however, to take care of
the different use of time ordered versus retarded Green functions. Subtle
questions concerning the precise definition of the equal time wave function
arise, because the wave function for the Coulomb gluon is discontinuous with
respect to the relative time of the gluon. A striking feature is that a one
loop non abelian graph contributes to the same order as tree graphs, because
the couplings of transverse gluons in the tree graphs are suppressed in the non
relativistic bound state, while the higher order loop graph can couple to
quarks via non suppressed Coulomb gluons. We also calculate the amplitude for
quark and antiquark at zero distance in the quark-glue-antiquark component of
the P-state. This quantity is of importance for annihilation decays of
P-states. It shows a remarkable compensation between the tree graph and the non
abelian loop graph contribution. An extension of our results to include non
perturbative effects is possible.Comment: 15 pages, 8 figure
Finite size corrections to disordered Ising models on Random Regular Graphs
We derive the analytical expression for the first finite size correction to
the average free energy of disordered Ising models on random regular graphs.
The formula can be physically interpreted as a weighted sum over all non
self-intersecting loops in the graph, the weight being the free-energy shift
due to the addition of the loop to an infinite tree
Contractible Theta Complexes of Graphs
We examine properties of graphs that result in the graph having a contractible theta complex. We classify such properties for tree graphs and graphs with one loop and we introduce examples of graphs with such properties for tree graphs and graphs with one or two loops. For more general graphs, we show that having a contractible theta complex is not an elusive property, and that any skeleton of a graph with at least three loops can be made to have a contractible theta complex by strategically adding vertices to its skeleton
Tree loop graphs
Many problems involving DNA can be modeled by families of intervals. However, traditional interval graphs do not take into account the repeat structure of a DNA molecule. In the simplest case, one repeat with two copies, the underlying line can be seen as folded into a loop. We propose a new definition that respects repeats and define loop graphs as the intersection graphs of arcs of a loop. The class of loop graphs contains the class of interval graphs and the class of circular-arc graphs. Every loop graph has interval number 2. We characterize the trees that are loop graphs. The characterization yields a polynomial-time algorithm which given a tree decides whether it is a loop graph and, in the affirmative case, produces a loop representation for the tree.Facultad de Ciencias Exacta
- …