Schwinger terms in 1+1 dimensions

Two different approaches — Källen’s and Brandt’s methods — for calculation of the Schwinger terms in the 1+1 dimensional Abelian and non-Abelian free current algebras are discussed. These methods are applied to calculation of the single and double commutators. The validity of the Jacobi identities is examined in 1+1 and 3+1 dimensions and in this way is given natural restriction on the regularization. It is shown that the Jacobi identity cannot be broken in 1+1 dimensions even using the regularization which fails in the 3+1 dimensional case. A connection between the Schwinger term and anomaly is shown in the simplest case of the Schwinger model.     

Dependence of the S-matrix on the choice of field variables in the effective Lagrangian

The dependence of the on-shellS-matrix on the change of the Lagrangian induced by a nonlinear substitutionF() is investigated by means of a graphical analysis. A cancellation mechanism is found and used to show that the tree approximation of theS-matrix is independent of such a substitution and that the Jacobian of the substitution has to be introduced in order to cancel a new class of singular one-loop graphs and to recover the primaryS-matrix at the one-loop level.     

The choice of spectroscopic scheme in x-ray plasma diagnostics

The ray tracing codes for flat, cylindrically bent (Johann horizontal focusing and von Hamos vertical focusing geometry), elliptically and spherically bent crystal spectrometers were developed. The codes, extended by introducing the two-dimensional source and the real shape of single crystal diffraction pattern in dependence on the radius of curvature, contribute to a proper choice of experimental configuration in x-ray plasma diagnostics. A method of ray tracing the von Hamos spectrometer is presented in detail. The use of the ray tracing code to the optimization of the spectroscopic scheme is demonstrated on the analysis of gas-puff z-pinch experiment.     

Detecting quantum states with a positive Wigner function beyond mixtures of Gaussian states

We propose a criterion giving a sufficient condition for quantum states of a harmonic oscillator not to be expressible as a convex mixture of Gaussian states. This nontrivial property is inherent to, e.g., a single-photon state and the criterion thus allows one to reveal a signature of the state even in quantum states with a positive Wigner function. The criterion relies on directly measurable photon number probabilities and enables detection of this manifestation of a single-photon state in quantum states produced by solid-state single-photon sources in a weak coupling regime.     

On stability of Raman and degenerate hyper-Raman scattering

The problem of the stationary generation by Raman and degenerate hyper-Raman scattering is solved by means of two methods: stationary solution of the generalized Fokker-Planck equation and linear analysis of stability of the Langevin equations. The conditions of stability and the corresponding stationary values for amplitudes of the Stokes, anti-Stokes or output laser modes are obtained for particular cases. A phenomenon analogous to the second order phase transition can occur for Stokes or anti-Stokes interaction of Raman scattering above the threshold value of the pump amplitude. The anti-Stokes interaction of degenerate hyper-Raman scattering can show bistable behaviour above the second threshold value of the pump amplitude.The author would like to express his sincere thanks to Dr. J. Peina for comments and stimulating discussions.     

Diffusion of titanium atoms in Ni-Si-B metallic glass

The diffusion ot Ti atoms in the Ni₇₇Si₃B₂₀ metallic glass was studied by the Auger electron spectroscopy. The temperature dependence of the diffusion coefficient obeys the Arrhenius relation with the activation energyE=1·7 eV and the pre-exponential factorD ₀=0·86 × ×10^–4 m² s^–1. Possible mechanisms of the atomic transport in metallic glasses are discussedThe authors wish to thank Dr. P. Duhaj for providing the metallic glass samples.     

High resolution spectroscopy of (lambda)(12)B by electroproduction

An experiment measuring electroproduction of hypernuclei has been performed in hall A at Jefferson Lab on a 12C target. In order to increase counting rates and provide unambiguous kaon identification two superconducting septum magnets and a ring imaging Cherenkov detector were added to the hall A standard equipment. An unprecedented energy resolution of less than 700 keV FWHM has been achieved. Thus, the observed (Lambda)(12)B spectrum shows for the first time identifiable strength in the core-excited region between the ground-state s-wave Lambda peak and the 11 MeV p-wave Lambda peak.     

Optimized t-expansion method for the Rabi Hamiltonian

A polemic arose recently about the applicability of the t-expansion method to the calculation of the ground state energy E₀ of the Rabi model. For specific choices of the trial function and very large number of involved connected moments, the t-expansion results are rather poor and exhibit considerable oscillations. In this Letter, we formulate the t-expansion method for trial functions containing two free parameters which capture two exactly solvable limits of the Rabi Hamiltonian. At each order of the t-series, E₀ is assumed to be stationary with respect to the free parameters. A high accuracy of E₀ estimates is achieved for small numbers (5 or 6) of involved connected moments, the relative error being smaller than ¹⁰−4 (0.01%) within the whole parameter space of the Rabi Hamiltonian. A special symmetrization of the trial function enables us to calculate also the first excited energy E₁, with the relative error smaller than ¹⁰−2 (1%).