Exact Nonperturbative Unitary Amplitudes for 1->N Transitions

I present an extension to arbitrary N of a previously proposed field theoretic model, in which unitary amplitudes for $1->8$ processes were obtained. The Born amplitude in this extension has the behavior $A(1->N)^{tree}\ =\ g^{N-1}\ N!$ expected in a bosonic field theory. Unitarity is violated when $|A(1->N)|>1$, or when $N>\N_crit\simeq e/g.$ Numerical solutions of the coupled Schr\"odinger equations shows that for weak coupling and a large range of N>\ncrit, the exact unitary amplitude is reasonably fit by a factorized expression |A(1->N)| \sim (0.73 /N) \cdot \exp{(-0.025/\g2)}. The very small size of the coefficient 1/\g2 , indicative of a very weak exponential suppression, is not in accord with standard discussions based on saddle point analysis, which give a coefficient $\sim 1.\$ The weak dependence on $N$ could have experimental implications in theories where the exponential suppression is weak (as in this model). Non-perturbative contributions to few-point correlation functions in this theory would arise at order $K\ \simeq\ \left((0.05/\g2)+ 2\ ln{N}\right)/ \ ln{(1/\g2)}$in an expansion in powers of$\g2.$Comment: 11 pages, 3 figures (not included

Properties of Nucleon Resonances by means of a Genetic Algorithm

We present an optimization scheme that employs a Genetic Algorithm (GA) to determine the properties of low-lying nucleon excitations within a realistic photo-pion production model based upon an effective Lagrangian. We show that with this modern optimization technique it is possible to reliably assess the parameters of the resonances and the associated error bars as well as to identify weaknesses in the models. To illustrate the problems the optimization process may encounter, we provide results obtained for the nucleon resonances $\Delta$(1230) and $\Delta$(1700). The former can be easily isolated and thus has been studied in depth, while the latter is not as well known experimentally.Comment: 12 pages, 10 figures, 3 tables. Minor correction

Lattice-corrected strain-induced vector potentials in graphene

The electronic implications of strain in graphene can be captured at low energies by means of pseudovector potentials which can give rise to pseudomagnetic fields. These strain-induced vector potentials arise from the local perturbation to the electronic hopping amplitudes in a tight-binding framework. Here we complete the standard description of the strain-induced vector potential, which accounts only for the hopping perturbation, with the explicit inclusion of the lattice deformations or, equivalently, the deformation of the Brillouin zone. These corrections are linear in strain and are different at each of the strained, inequivalent Dirac points, and hence are equally necessary to identify the precise magnitude of the vector potential. This effect can be relevant in scenarios of inhomogeneous strain profiles, where electronic motion depends on the amount of overlap among the local Fermi surfaces. In particular, it affects the pseudomagnetic field distribution induced by inhomogeneous strain configurations, and can lead to new opportunities in tailoring the optimal strain fields for certain desired functionalities.Comment: Errata for version

The Galaxy Octopole Moment as a Probe of Weak Lensing Shear Fields

In this paper, we introduce the octopole moment of the light distribution in galaxies as a probe of the weak lensing shear field. While traditional ellipticity estimates of the local shear derived from the quadrupole moment are limited by the width of the intrinsic ellipticity distribution of background galaxies, the dispersion in the intrinsic octopole distribution is expected to be much smaller, implying that the signal from this higher order moment is ultimately limited by measurement noise, and not by intrinsic scatter. We present the computation of the octopole moment and show that current observations are at the regime where the octopole estimates will soon be able to contribute to the overall accuracy of the estimates of local shear fields. Therefore, the prospects for this estimator from future datasets like the Advanced Camera for Survey and the Next Generation Space Telescope are very promising.Comment: 9 pages, 2 PostScript figures; Submitted to Astrophysical Journa

Diffraction of wave packets in space and time

The phenomenon of wave packet diffraction in space and time is described. It consists in a diffraction pattern whose spatial location progresses with time. The pattern is produced by wave packet quantum scattering off an attractive or repulsive time independent potential. An analytical formula for the pattern at $t\to\infty$ is derived both in one dimension and in three dimensions. The condition for the pattern to exist is developed. The phenomenon is shown numerically and analytically for the Dirac equation in one dimension also. An experiment for the verification of the phenomenon is described and simulated numerically.Comment: replaces quant-ph 0008077, 0008107, Journal of physics, A, in pres

Some Properties of Amplitudes at Multi Boson Thresholds in Spontaneously Broken Scalar Theory

It is shown that in a $\lambda \phi^4$ theory of one real scalar field with spontaneous breaking of symmetry a calculation of the amplitudes of production by a virtual field $\phi$ of $n$ on-mass-shell bosons all being exactly at rest is equivalent in any order of the loop expansion to a Euclidean space calculation of the mean field of a kink-type configuration. Using this equivalence it is found that all the $1 \to n$ amplitudes have no absorptive part at the thresholds to any order of perturbation theory. This implies non-trivial relations between multi-boson threshold production amplitudes. In particular the on-mass-shell amplitude of the process $2 \to 3$ should vanish at the threshold in all loops. It is also shown that the factor $n!$ in the $1 \to n$ amplitudes at the threshold is not eliminated by loop effects.Comment: 11 pages including 3 figures, LaTeX, TPI-MINN-92/61-

Surface criticality in random field magnets

The boundary-induced scaling of three-dimensional random field Ising magnets is investigated close to the bulk critical point by exact combinatorial optimization methods. We measure several exponents describing surface criticality: $\beta_1$ for the surface layer magnetization and the surface excess exponents for the magnetization and the specific heat, $\beta_s$ and $\alpha_s$. The latter ones are related to the bulk phase transition by the same scaling laws as in pure systems, but only with the same violation of hyperscaling exponent $\theta$ as in the bulk. The boundary disorders faster than the bulk, and the experimental and theoretical implications are discussed.Comment: 6 pages, 9 figures, to appear in Phys. Rev.