Energy-level statistics of model quantum systems: Universality and scaling in a lattice-point problem

We investigate the statistics of the numberN(R, S) of lattice pointsnZ ², in an annular domain (R, w)=(R+w)A\RA, whereR, w>0. HereA is a fixed convex set with smooth boundary andw is chosen so that the area of (R, w) isS. The statistics comes fromR being taken as random (with a smooth density) in some interval [c ₁ T,c ₂,T],c ₂>c ₁>0. We find that in the limitT the variance and distribution of N=N(R; S)–S depend strongly on howS grows withT. There is a saturation regimeS/T, asT, in which the fluctuations in N coming from the two boundaries of are independent. Then there is a scaling regime,S/Tz, 0<z<, in which the distribution depends onz in an almost periodic way going to a Gaussian asz0. The variance in this limit approachesz for genericA, but can be larger for degenerate cases. The former behavior is what one would expect from the Poisson limit of a distribution for annuli of finite area.     

Symmetry of electronic states in garnets

The paper presents the classification of the electronic empty lattice eigenvalues and the classification of the Bloch sums for the garnet structureIa3d (O _h ¹⁰ ) at the symmetry points, H, P, andN of the Brillouin zone. This provides a starting point for the energy band studies of these technologically important materials.The author thanks Dr. V. Frei for useful comments.     

Complex supersymmetry and supersymmetric skyrmion

Starting from the complex supersymmetry and showing that the stabilizing term is directly present in the kinetic term of the vector superfield, we show a possibility to obtain supersymmetric skyrmion.     

Common-path achromatic rotational-shearing coronagraph

To suppress starlight for direct exoplanet observation, we propose a common-path achromatic rotational-shearing coronagraph (CP-ARC), which is an interferocoronagraph with an angular-adjustable field rotator. The CP-ARC aims to maintain unwanted detection of stellar light, which can be suppressed incompletely by interference because of the finite diameter of the star. Compared to the previous interferocoronagraph, which had a nonadjustable 180° field rotation, the proposed CP-ARC can improve the coronagraphic contrast by several orders if the CP-ARC is combined with medium or large telescopes where the companion-star separation is optically resolved by more than a few Airy radii. The CP-ARC is made robust against mechanical disturbances due to the common-path interferometer principle.     

Self-focusing of femtosecond diffraction-resistant vortex beams in water

We report experiments on self-focusing of femtosecond diffraction-resistant vortex beams in water. These beams are higher-order Bessel beams with weak azimuthal modulation of the transverse intensity patterns. The modulation overrides the self-focusing dynamics and results in the formation of regular bottlelike filament distributions. The peak-power thresholds for filamentation, at a particular distance, are relatively accurately estimated by the adaptation of the Marburger formula derived earlier for Gaussian beams. The nonlinear conversion of the incident conical waves into the localized spatial wave packets propagating near the beam axis is observed.     

Advection of a passive vector field by the Gaussian velocity field with finite correlations in time

Using the field theoretic renormalization group technique the model of a passive vector field advected by an incompressible turbulent flow is investigated up to the second order of the perturbation theory (two-loop approximation). The turbulent environment is given by statistical fluctuations of the velocity field that has a Gaussian distribution with zero mean and defined noise with finite correlations in time. Two-loop analysis of all possible scaling regimes in general d-dimensional space is done in the plane of exponents ? ? η, where ? characterizes the energy spectrum of the velocity field in the inertial range E ∝ k ^{1 ? 2ε}, and η is related to the correlation time at the wave number k which is scaled as k ^{?2 + η}. It is shown that the scaling regimes of the present model of vector advection have essentially different properties than the scaling regimes of the corresponding model of passively advected scalar quantity. The results demonstrate the fact that within the present model of passively advected vector field the internal tensor structure of the advected field can have nontrivial impact on the diffusion processes deep inside in the inertial interval of given turbulent flow.     

Interaction Products of 12·5 Deuterons with Molybdenum and their Isolation Possibilities from Worn-out Cyclotron Parts

Using chemical separations and radiometric measurements medium-half-life irradiation products of molybdenum with 12.5 MeV deuterons were determined (⁹⁰Nb, ⁹²Nb, ^95mNb, ⁹⁵Nb, ⁹⁶Nb, ⁹⁹Mo, ^95mTc, ⁹⁶Tc, ^99mTc) as well as thick target yields for some of them: ⁹²Nb (0.22 μCi/μAh), ⁹⁵Nb(0.05 μCi/μAh), ⁹⁹Mo (64 μCi/μAh), ^95mTc(0.76 μCi/μAh), ⁹⁶Tc((62.5 μCi/μAh). Moreover isolation possibiities of radioactive preparations from removed worn-cut molybdenum parts of the U-120 cycletron are discussed.     

Observation and theoretical description of periodic geometric rearrangement in electronically excited nonstoichiometric sodium-fluoride clusters

We present two-color fs pump-probe spectra of Na2F which were recorded by employing excitation wavelengths around 1208 nm (pump) and ionization wavelengths around 405 nm (probe). The observed oscillatory structure of the signal with a period of 185 fs shows an excellent agreement with our simulated spectra. The employed ab initio Wigner distribution approach provides clear evidence that this observation is caused by photoinduced metal bond breaking followed by a butterfly-type periodic geometric rearrangement.     

On unconstrained SU(2) gluodynamics with theta angle

The Hamiltonian reduction of classical SU(2) Yang–Mills field theory to the equivalent unconstrained theory of gauge invariant local dynamical variables is generalized to the case of nonvanishing -angle. It is shown that for any -angle the elimination of the pure gauge degrees of freedom leads to a corresponding unconstrained non-local theory of self-interacting second rank symmetric tensor fields, and that the obtained classical unconstrained gluodynamics with different -angles are canonically equivalent as on the original constrained level. Received: 16 November 2001 / Published online: 5 April 2002