Recovering singularities of a potential from singularities of scattering data

In this paper we show that the leading singularities of certain potentials can be determined from the leading singularities of the backscattering (as well as other determined sets of scattering data). The potentials in question are conormal with respect to smooth surfaces of arbitrary dimension; the restrictions on their orders allow for unbounded potentials in all dimension greater than or equal to three.Partially supported by NSF Grant DMS-9101298 and an Alfred P. Sloan Research FellowshipPartially supported by NSF Grant DMS-9100178     

From scattering singularities to the partition of a horseshoe

In a chaotic scattering system there are two different approaches to construct a symbolic dynamics. One comes from the branching tree obtained from a scattering function. The other comes from a Markov partition based on the line of primary homoclinic tangencies in the Poincare map taken in the interaction region. In general the two results only coincide for a complete horseshoe. We show how to make a different choice for the partition in the internal Poincare section based on scattering behavior and not on homoclinic tangencies. Then the corresponding symbolic dynamics coincides also for the incomplete case with the one obtained naturally from the scattering functions. The scattering based partition lines of the horseshoe are constructed by an iterative procedure. (c) 1999 American Institute of Physics.     

High-energy scattering in QCD and cross singularities of Wilson loops

We consider elastic quark-quark scattering at high energy and fixed transferred momentum. Performing factorization of soft-gluon exchanges into the Wilson-line expectation value we find that there is one-to-one correspondence between high-energy asymptotics in QCD and renormalization properties of the so-called cross singularities of the Wilson lines. Using this relation we show that the asymptotic behavior of the quark-quark scattering amplitude is controlled by a 2 × 2 matrix of the cross anomalous dimensions. We evaluate the matrix of the cross anomalous dimension to two-loop order and study the properties of the obtained expressions to higher loop order.     

Resonance propagation in heavy-ion scattering

The formalism developed earlier by us for the propagation of a resonance in the nuclear medium in proton-nucleus collisions has been modified to the case of vector boson production in heavy-ion collisions. The formalism includes coherently the contribution to the observed di-lepton production from the decay of a vector boson inside as well as outside the nuclear medium. The medium modification of the boson is incorporated through an energy dependent optical potential. The calculated invariant ρ mass distributions are presented for the ρ-meson production using optical potentials estimated within the VDM and the resonance model. The shift in the invariant mass distribution is found to be small. To achieve the mass shift (of about 200 MeV towards lower mass) as indicated in the high energy heavy-ion collision experiments, an unusually strong optical potential of about −120 MeV is required. We also observe that, for not so heavy nuclear systems and/or for fast moving resonances, the shape, magnitude and peak position of the invariant mass distribution is substantially different if the contributions from the resonance decay inside and outside are summed-up at the amplitude level (coherently) or at the cross section level (incoherently).     

Complex singularities of the fluid velocity autocorrelation function

There are intensive debates regarding the nature of supercritical fluids: if their evolution from liquid-like to gas-like behavior is a continuous multistage process or there is a sharp well-defined crossover. Velocity auto-correlation function Z is the established detector of evolution of fluid particles dynamics. Usually, complex singularities of correlation functions give more information. For this reason, we investigate Z in complex plane of frequencies using numerical analytic continuation. We have found that naive picture with few isolated poles fails describing Z(ω) of one-component Lennard-Jones (LJ) fluid. Instead, we see the singularity manifold forming branch cuts extending approximately parallel to the real frequency axis. That suggests LJ velocity autocorrelation function is a multivalued function of complex frequency. The branch cuts are separated from the real axis by the well-defined “gap” whose width corresponds to an important time scale of a fluid characterizing crossover of system dynamics from kinetic to hydrodynamic regime. Our working hypothesis is that the branch cut origin is related to competition between one-particle dynamics and hydrodynamics. The observed analytic structure of Z is very stable under changes in the temperature; it survives at temperatures two orders of magnitude higher than the critical one.     

Resonance theory in atom-surface scattering

We study the problem of analytic extension of the resolvent for Hamiltonians arising in scattering of atoms by a quantum surface. We prove that the resolvent extends holomorphically to some regions of the lower half plane with isolated singularities called Landau resonances which are branch points of the resolvent. We study also the effect of impurities on the singularities of the resolvent and show that the presence of impurities adds poles to the Landau resonances.     

Singularities and accumulation of singularities of πN scattering amplitudes

It is demonstrated that for the isospin I = 1/2 πN scattering amplitude, T^I=1/2(s, t), $s={\left({m}_{N}^{2}-{m}_{\pi }^{2}\right)}^{2}/{m}_{N}^{2}$ and $s={m}_{N}^{2}+2{m}_{\pi }^{2}$ are two accumulation points of poles on the second sheet of complex s plane, and are hence accumulation of singularities of T^I=1/2(s, t). For T^I=3/2(s, t), $s={\left({m}_{N}^{2}-{m}_{\pi }^{2}\right)}^{2}/{m}_{N}^{2}$ is the accumulation point of poles on the second sheet of the complex s plane. The proof is valid up to all orders of chiral expansions.     

钠分子的共振喇曼散射

本文用80mW6238.2(?)的He-Ne激光激发钠蒸气,用一种新颖的棱镜反射光路,从后向首次观察到了56O0～8200(?)钠分子的共振喇曼谱.     

Resonance and scattering in microstructured optical fibers

We present an investigation into the mechanism for guidance of microstructured optical fibers consisting of high-refractive-index cylinders embedded in a low-index background. A new guidance regime is identified in which the fibers' confinement losses depend strongly on wavelength and the positions of the loss minima and maxima depend on the scattering properties of individual cylinders and only weakly on their position and number. We point out similarities between these results and those reported recently for two-dimensional antiresonant reflecting waveguides.     

S-Matrix singularities in scattering of charged particles on hydrogen-like targets

The scattering of a charged particle on an excited degenerate state of a hydrogen-like system is considered. The threshold and angular singularities of binary scattering amplitudes in this problem are studied. For these singularities closed-form analytical representations are obtained.     

Resonance Raman scattering in rare-earth tantalates

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 49, No. 6, pp. 998–1001, December, 1988.     

Resonance eigenfunctions in chaotic scattering systems

We study the semiclassical structure of resonance eigenstates of open chaotic systems. We obtain semiclassical estimates for the weight of these states on different regions in phase space. These results imply that the long-lived right (left) eigenstates of the non-unitary propagator are concentrated in the semiclassical limit ħ → 0 on the backward (forward) trapped set of the classical dynamics. On this support the eigenstates display a self-similar behaviour which depends on the limiting decay rate.     

Resonance Raman scattering at the saddle points of semiconductors

An approximate theory is formulated to describe resonance Raman scattering near the critical points of semiconductors using a model density of states. Large resonance enhancements and absolute scattering cross sections are predicted near the saddle points.     

Resonance structure of the beta-strength function

The beta-decay strength function S _β(E) is described within two approaches: numerical solution of equation of the theory of finite Fermi systems for the effective nuclear field and solution of these equations using the quasi-classical approximation. Calculations were carried out for the isotopes ⁷¹Ge and ¹²⁷Xe. A comparison with experimental data showed their good accuracy. The resonance structure of the function S _β(E) and the quenching-effect resulting from the effective charge of quasiparticles in the nucleus are discussed.     

Resonance phenomena and threshold features in positron—helium scattering

Investigations of resonances and threshold behaviors in positron-helium scattering have been made using the momentum-space coupled-channels optical method.The positronium formation channels are considered via an equivalent-local complex potential.The s-wave resonances and the Wigner cusp feature at the positronium(n = 1) formation threshold are compared with the previous reports.The p-and the d-wave resonances and a Wigner cusp feature at the positronium(n = 2) formation threshold are reported for the first time.     

Three-body scattering at positive energies: Solving the problem of moving logarithmic singularities

For three-body scattering at positive total energies, integral equations are obtained whose kernels have no logarithmic singularities on the contour of integration. The corresponding singularities that are present in original integral equations can be circumvented by shifting a part of the contour of integration from the real axis to the complex plane. This is done only for a special auxiliary solution appearing to be an analytic function in this region. The physical amplitude proper is found as one of the solutions to the resulting set of equations. In contrast to conventional techniques, an additional analysis is therefore not required here, so that numerical solutions can be obtained within standard computational schemes.     

The physical meaning of scattering matrix singularities in coupled-channel formalisms⋆

The physical meaning of bare and dressed scattering matrix singularities has been investigated. Special attention has been attributed to the role of the well-known invariance of the scattering matrix with respect to the field transformation of the effective Lagrangian. Examples of evaluating bare and dressed quantities in various models are given.