Correlation widths in quantum-chaotic scattering

An important parameter to characterize the scattering matrix S   for quantum-chaotic scattering is the width Γcorr${\Gamma }_{\mathrm{corr}}$ of the S  -matrix autocorrelation function. We show that the “Weisskopf estimate” d/(2π)c_∑Tc$d/(2\pi ){\sum }_c{T}_c$ (where d   is the mean resonance spacing, Tc$T_c$ with 0?Tc?1$0?T_c?1$ the “transmission coefficient” in channel c   and where the sum runs over all channels) provides a good approximation to Γcorr${\Gamma }_{\mathrm{corr}}$ even when the number of channels is small. That same conclusion applies also to the cross-section correlation function.     

Lower bounds for Wiener integrals

Techniques are developed to sharpen lower bounds for density matrices occurring in statistical mechanics. The Wiener integrals are treated by insertion of trial functionals and parametric representations of unity that involve functionals of the path. Jensen's inequality is applied to suitable parameter-dependent path measures. These yield stronger forms than the basic Feynman bound. We also introduce trajectory insertions, and use coupling constant integration and the hierarchy for correlation functions to improve the bounds.     

Causality bounds for neutron-proton scattering

We consider the constraints of causality and unitarity for the low-energy interactions of protons and neutrons. We derive a general theorem that non-vanishing partial-wave mixing cannot be reproduced with zero-range interactions without violating causality or unitarity. We define and calculate interaction length scales which we call the causal range and the Cauchy-Schwarz range for all spin channels up to J = 3 . For some channels we find that these length scales are as large as 5fm. We investigate the origin of these large lengths and discuss their significance for the choice of momentum cutoff scales in effective field theory and universality in many-body Fermi systems.     

Lower bounds for the electric susceptibility

New lower bounds for the susceptibility in terms of the first and second moments are derived. These lower bounds are applied in the problem of the electric susceptibility.     

Landau levels line widths in potential scattering in the presence of a strong magnetic field

Summary The FBA scattering cross-section in the presence of a strong magnetic field diverges at the Landau thresholds. Such divergences are eliminated by the introduction of a modified density of states, accounting for the finite Landau states lifetime of the electrons in a magnetized plasma.     

Generalized diffusion and quasi-elastic scattering widths in two-dimensional systems

The paper presents approximate calculations of dimensionality and lattice symmetry effects in the wave vector and frequency dependent diffusional response of disordered lattices. Numerical results are given and comparatively discussed for the tracer diffusion correlation function and the quasi-elastic incoherent scattering width in triangular, simple square and simple cubic lattices, only the restriction of double occupancy avoidance being taken into account. The quasi-elastic coherent scattering width is estimated for a triangular system possessing liquid-like structural disorder by means of the simple inclusion of a spread in jump lengths around a preferred set of jumps. Qualitative contact is made with recent neutron scattering experiments on alkali-metal graphite intercalation compounds.     

Statistical properties of resonance widths for open quantum graphs

We connect quantum compact graphs with infinite leads, and turn them into scattering systems. We derive an exact expression for the scattering matrix, and explain how it is related to the spectrum of the corresponding closed graph. The resulting expressions allow us to get a clear understanding of the phenomenon of resonance trapping due to over-critical coupling with the leads. Finally, we analyse the statistical properties of the resonance widths and compare our results with the predictions of random matrix theory. Deviations appearing due to the dynamical nature of the system are pointed out and explained.     

Statistical properties of resonance widths for open quantum graphs

We connect quantum compact graphs with infinite leads, and turn them into scattering systems. We derive an exact expression for the scattering matrix, and explain how it is related to the spectrum of the corresponding closed graph. The resulting expressions allow us to get a clear understanding of the phenomenon of resonance trapping due to over-critical coupling with the leads. Finally, we analyse the statistical properties of the resonance widths and compare our results with the predictions of random matrix theory. Deviations appearing due to the dynamical nature of the system are pointed out and explained.     

Distribution of resonance widths in localized tight-binding models

We numerically analyze the distribution of scattering resonance widths in one- and quasi-one dimensional tight binding models, in the localized regime. We detect and discuss an algebraic decay of the distribution, similar, though not identical, to recent theoretical predictions. Received 14 April 2000 and Received in final form 27 July 2000     

Optimum and standard beam widths for numerical modeling of interface scattering problems

Gaussian beams provide a useful insonifying field for surface or interface scattering problems such as encountered in electromagnetics, acoustics and seismology. Gaussian beams have these advantages: (i) They give a finite size for the scattering region on the interface. (ii) The incident energy is restricted to a small range of grazing angles. (iii) They do not have side lobes. (iv) They have a convenient mathematical expression. The major disadvantages are: (i) Insonification of an interface is nonuniform. The scattered field will depend on the location of the scatterers within the beam. (ii) The beams spread, so that propagation becomes an integral component of the scattering problem. A standard beam parameterization is proposed which keeps propagation effects uniform among various models so that the effects of scattering only can be compared. In continuous wave problems, for a given angle of incidence and incident amplitude threshold, there will be an optimum Gaussian beam which keeps the insonified area as small as possible. For numerical solutions of pulse beams, these standard parameters provide an estimate of the smallest truncated domain necessary for a physically meaningful result.     

The isospin bounds and phase-contours in pion-nucleon scattering

In this paper we investigate the isospin constraints on differential and integrated (unpolarized and polarized) cross sections in pion-nucleon scattering. Defining$\text{Σ}{}^{\mathrm{(n)}}\text{-}\text{integrated}$ cross sections and using the classical Minkowski and Hölder inequalities we obtain a large class of isospin bounds. The saturation of the isospin bounds is investigated using dispersion relation predictions and a CERN theoretical solution for the phase shifts.     

Non-hermitean delocalization: Multiple scattering and bounds

We study localization and delocalization in a class of non-hermitean Hamiltonians inspired by the problem of vortex pinning in superconductors. We show how to take into account multiple scattering. We also obtain some bounds on the complex energy spectrum.     

Anomalous resonance effects in collision broadened spectral line widths

Calculations of self broadened DF vibration-rotation line widths and of widths of DF and HF broadened by each other have been performed using the Anderson theory. The calculations include effects of inexact resonances in the upper states of the fundamental band and also include dipole-dipole, dipole-quadropole and the quadropole-quadropole terms in the multipolar expansion. A qualitative discussion of the results is given.     

Distribution of resonance widths and dynamics of continuum coupling

We analyze the statistics of resonance widths in a many-body Fermi system with open decay channels. Depending on the strength of continuum coupling, such a system reveals growing deviations from the standard chi-square (Porter-Thomas) width distribution. The deviations emerge from the process of increasing interaction of intrinsic states through common decay channels; in the limit of perfect coupling this process leads to the superradiance phase transition. The width distribution depends also on the intrinsic dynamics (chaotic versus regular). The results presented here are important for understanding the recent experimental data concerning the width distribution for neutron resonances in nuclei.     

Lower bounds for the surface energy of two-dimensional foams

Amongst the two-dimensional cellular patterns that fill a plane, dry foams at stable equilibrium typify a particular subset for which the total perimeter P of cell boundaries ( i.e., films between bubbles) has a local minimum. For a given set of bubble areas Ai (i=1,..., N), P can be written in the form P=R(SigmaN(i=1) square root Ai)/2, where R is topology dependent. We seek the set of areas Ai and the cluster topology that minimise R, and propose lower bounds for R that set lower bounds for the surface energy of i) individual bubbles, with circular edges meeting at 2pi/3 angles at vertices (Plateau cells), and ii) infinite periodic bubble clusters.     

Lower bounds for the surface energy of two-dimensional foams

The European Physical Journal E - Amongst the two-dimensional cellular patterns that fill a plane, dry foams at stable equilibrium typify a particular subset for which the total perimeter P of cell...     

Lower bounds for the eigenvalues of the Dirac operator

On a compact Riemannian spin manifold we give new lower bounds for the eigenvalues of the Dirac operator in terms of the curvature and of the norm of an appropriate endomorphism of the tangent bundle. As a corollary, one gets all known results in this direction. The limiting-case is then studied.     

Factorization method for inverse obstacle scattering problem in three-dimensional planar acoustic waveguides

In this paper, we consider the inverse scattering problem of reconstructing a bounded obstacle in a three-dimensional planar waveguide from the scattered near-field data measured on a finite cylindrical surface containing the obstacle and corresponding to infinitely many incident point sources also placed on the measurement surface. The obstacle is allowed to be an impenetrable scatterer or a penetrable scatterer. We establish the validity of the factorization method with the nearfield data to characterize the obstacle in the planar waveguide by constructing an outgoing-to-incoming operator which is an integral operator defined on the measurement surface with the kernel given in terms of an infinite series.