Resonant interband scattering of image-potential states

Image-potential states in front of a clean Cu (100) surface were investigated by time- and angle-resolved two-photon photo-emission (2PPE). We observe a previously unknown quasi-elastic relaxation channel, which efficiently couples states with different quantum numbers, n, and parallel momenta, k_∥. This process of resonant interband scattering (RIS) is independent of sample temperature and shows a close relationship to the pure dephasing of image-potential states. Received: 1 October 2001 / Revised version: 24 October 2001 / Published online: 23 November 2001     

Cutoff dependence of the Casimir effect

The problem of calculating the Casimir force on two conducting planes by means of the stress tensor is examined. The evaluation of this quantity is carried out using an explicit regularization procedure which has its origin in the underlying (2+1) dimensional Poincaré invariance of the system. The force between the planes is found to depend on the ratio of two independent cutoff parameters, thereby rendering any prediction for the Casimir effect an explicit function of the particular calculational scheme employed. Similar results are shown to obtain in the case of the conducting sphere. Received: 15 October 2000 / Revised version: 10 January 2001 / Published online: 6 April 2001     

Study of the O(N) linear \sigma model at finite temperature using the 2PPI expansion

We show that a new expansion, which sums seagull and bubble graphs to all orders, can be applied to the O(N) linear -model at finite temperature. We prove that this expansion can be renormalized with the usual counterterms in a mass independent scheme and that Goldstone's theorem is satisfied at each order. At the one loop order of this expansion, the Hartree result for the effective potential (daisy and superdaisy graphs) is recovered. We show that at one loop 2PPI order, the self-energy of the -meson can be calculated exactly and that diagrams are summed beyond the Hartree approximation. Received: 22 March 2001 / Revised version: 3 September 2001 / Published online: 14 December 2001     

Quantum Morphing and the Jones Polynomial

We will explore the experimental observation that on the set of knots with bounded crossing number, algebraically independent Vassiliev invariants become correlated, as noticed first by S. Willerton. We will see this through the value distribution of the Jones polynomial at roots of unit. As the degree of the roots of unit is getting larger, the higher order fluctuation is diminishing and a more organized shape will emerge from a rather random value distribution of the Jones polynomial. We call such a phenomenon “quantum morphing”. Evaluations of the Jones polynomial at roots of unity play a crucial role, for example in the volume conjecture. Received: 15 February 2001 / Accepted: 8 June 2001     

Is the axial anomaly really determined in a continuous non-perturbative regularization?

In the framework of a gauge invariant continuous and non-perturbative regularization scheme based on the smearing of point-like interactions by means of cutoff functions, we show that the axial anomaly, though cutoff independent, depends on the shape of the cutoff functions. The standard value for the strength of the axial anomaly is recovered if we assume that the regularized gauge invariant axial current is in addition local. Received: 11 July 2001 / Published online: 25 January 2002     

Direct determination of the CKM matrix from decays of W Bosons and top quarks at high energy \mathbf{e}^+\mathbf{e}^- colliders

At proposed high energy linear colliders a large number of W bosons and top quarks will be produced. We evaluate the potential precision to which the decay branching ratios into the various quark species can be measured, implying also the determination of the respective CKM matrix elements. Crucial is the identification of the individual quark flavours, which can be achieved independent of QCD models. For transitions involving up quarks the accuracy is of the same order of magnitude as has been reached in hadron decays. We estimate that for charm transitions a precision can be reached that is superior to current and projected traditional kinds of measurements. The determination will be significantly improved, and for the first time a direct measurement of the transition can be made. In all cases such a determination is complementary to the traditional way of extracting the CKM matrix elements. Received: 1 February 2001 / Revised version: 21 May 2001 / Published online: 19 July 2001     

On the Integrated Density of States for Schrödinger Operators on ℤ2 with Quasi Periodic Potential

In this paper we consider discrete Schr?dinger operators on the lattice ℤ² with quasi periodic potential. We establish new regularity results for the integrated density of states, as well as a quantitative version of a “Thouless formula”, as previously considered by Craig and Simon, for real energies and with rates of convergence. The main ingredient is a large deviation theorem for the Green's function that was recently established by Bourgain, Goldstein, and the author. For the integrated density of states an argument of Bourgain is used. Finally, we establish certain fine properties of separately subharmonic functions of two variables that might be of independent interest. Received: 13 February 2001 / Accepted: 21 May 2001     

The annihilation of virtual photons into pseudoscalar mesons

We investigate the possibility to constrain the pion distribution amplitude from the transition. For a surprisingly large range in the two photon virtualities we find that the transition form factor is essentially independent of the distribution amplitude. This in turn entails a parameter-free prediction of QCD. The form factors are also briefly discussed. We estimate that experimental studies might be feasible at the existing experiments BaBar, Belle, and CLEO. Received: 30 August 2001 / Published online: 23 November 2001     

Direct dark matter investigation

Experimental efforts and theoretical developments support that most of the Universe is dark and a large fraction of it should be made of relic particles; many possibilities are open on their nature and interaction types. This motivates experimental efforts to investigate the direct detection of these particles with various techniques. In particular, experiments offering a model independent signature for the presence of Dark Matter (DM) particles in the Galactic halo are mandatory. In this paper some general arguments will be summarized and particular care will be given to the results obtained by the DAMA/LIBRA experiment (sensitive mass: ～250 kg) at the Gran Sasso National Laboratory of the I.N.F.N. by exploiting the model independent DM annual modulation signature with higly radiopure NaI(Tl) target-detectors. Cumulatively with the former DAMA/NaI (sensitive mass: ～100 kg) an exposure of 1.17 ton yr, collected over 13 annual cycles, has been released so far; a model independent evidence of the presence of DM particles in the galactic halo is supported at 8.9 ρ confidence level (C.L.). In addition, experimental and theoretical uncertainties and their implications in the interpretation and comparison of different kinds of results will be shortly addressed. Some perspectives will be mentioned.     

Infrared picosecond absorption spectroscopy of microcrystalline silicon: separation between carrier recombination in crystalline and amorphous fractions

We have studied ultra-fast carrier dynamics of photo-excited carriers in hydrogenated microcrystalline silicon prepared by a very high frequency glow-discharge technique. We report on direct observation of two types of dynamics using selective photo-excitation in picosecond pump and probe measurements. One type of the observed dynamics has been found to be independent of the sample preparation, while the other reflects the relative weights of crystalline and amorphous fractions. We propose a simple rate-equation model that describes the carrier dynamics in microcrystalline silicon in terms of the composition of those in Si microcrystallites and in the a-Si:H tissue which surrounds the microcrystallites. The model without any fitting parameters reproduces the experimental data very well when the dynamics are scaled with relative volume fractions as obtained from Raman spectra. Received: 23 November 2000 / Accepted: 17 March 2001 / Published online: 23 May 2001     

Magnetic interface polarization of the La-5d states in Fe/LaHx multilayers

For rare-earth (RE)-hydrides (REHx), a metal-to-insulator transition is observed if the hydrogen concentration is increased from the dihydride (x=2) towards the trihydride (x=3). This transition provides an object for studies of the magnetic interface polarization in layered ferromagnet/insulator structures. For different samples with a fixed Fe and varied LaH_x sublayer thickness t_LaHx ([15 ? Fe/t? LaH_x]xn), the H concentration x in the LaH_x sublayer is gradually increased in the experiment. Starting from the as prepared dihydride REH_2-δ, the modification of the magnetic polarization of the La-5d states at the Fe/La_x interface is studied across the transition by magnetic circular dichroism measurements at the La-L₂ and L₃ edges. The experiments reveal an induced magnetic polarization of the La-5d hole states on a length scale of 9 ? that is independent of the altered electronic structure of the La-5d states. Received: 23 May 2001 / Accepted: 4 July 2001 / Published online: 5 October 2001     

Mean-Field Criticality for Percolation on Planar Non-Amenable Graphs

The critical exponents β, γ, δ and Δ are proved to exist and to take their mean-field values for independent percolation on the following classes of infinite, locally finite, connected transitive graphs: (1) Non-amenable planar with one end. (2) Unimodular with infinitely many ends. Received: 4 April 2001 / Accepted: 4 October 2001     

Effective A-state fluorescence lifetime of formaldehyde in atmospheric pressure CH4/air flames

Using excitation pulses of ∼30-ps duration and a fast photomultiplier detector, effective fluorescence lifetimes of the A-stateof formaldehyde after excitation at 355 and 339 nm have been measured in the preheating zone of an atmospheric pressure, premixed methane/air flame. The fluorescence lifetimes were determined as a function of height above the exit of a slot burner and were thus probed in regions of varying gas temperature and composition. The fluorescence lifetimes were independent of the intensity of the excitation pulse and decreased as a function of height in the burner from ∼18±8 ns at 1.2 mm down to 7±1 ns at 3.8 mm. This trend of the effective fluorescence lifetime with composition and temperature in the flame can qualitatively be reproduced using calculated major species mole fractions and species-specific quenching cross sections for CH from the literature. Received: 13 June 2001 / Revised version: 27 September 2001 / Published online: 29 November 2001     

A superspace embedding of the Wess–Zumino model

We embed the Wess–Zumino (WZ) model in a wider superspace than the one described by chiral and anti-chiral superfields. Received: 19 June 2001 / Revised version: 19 September 2001 / Published online: 21 November 2001     

Integrable Structure of the Dirichlet Boundary Problem in Two Dimensions

We study how the solution of the two-dimensional Dirichlet boundary problem for smooth simply connected domains depends upon variations of the data of the problem. We show that the Hadamard formula for the variation of the Dirichlet Green function under deformations of the domain reveals an integrable structure. The independent variables corresponding to the infinite set of commuting flows are identified with harmonic moments of the domain. The solution to the Dirichlet boundary problem is expressed through the tau-function of the dispersionless Toda hierarchy. We also discuss a degenerate case of the Dirichlet problem on the plane with a gap. In this case the tau-function is identical to the partition function of the planar large N limit of the Hermitian one-matrix model. Received: 18 September 2001 / Accepted: 18 December 2001     

Factorial correlators: angular scaling within QCD jets

Factorial correlators measure the amount of dynamical correlation in the multiplicity between two separated phase-space windows. We present the analytical derivation of factorial correlators for a QCD jet described at the double logarithmic (DL) accuracy. We obtain a new angular scaling property for properly normalized correlators between two solid-angle cells or two rings around the jet axis. Normalized QCD factorial correlators scale with the angular distance and are independent of the window size. Scaling violations are expected beyond the DL approximation, in particular from the subjet structure. Experimental tests are feasible, and thus would be welcome. Received: 12 January 2001 / Published online: 7 September 2001     

Determination of the dielectric function of porous silicon by high-order laser-harmonic radiation

Porous-silicon reflectance has been determined over a large energy range, from 1 eV to 16 eV, by combining a NIR/visible/UV spectrometer with a new VUV light source as laser-harmonic radiation. The porous-silicon dielectric function was deduced from reflectance measurements by Kramers–Kronig analysis. We point out that, for the first time, laser harmonics have been applied in the optical characterization of materials as a new and suitable alternative to synchrotron radiation. Received: 9 January 2001 / Accepted: 28 April 2001 / Published online: 20 June 2001     

Flexible all-plastic mirrors for the THz range

We present a simple and cheap approach to fabricate large-area stop-band filters and mirrors for the THz range. This approach extends the well-known concept of dielectric mirrors to the far infrared. We use alternating layers of different polymer materials with a typical thickness of several tens of micrometers to build a flexible all-plastic mirror. The structures are characterized by THz time-domain spectroscopy. The experimental results are in good agreement with transfer-matrix simulations. Received: 28 September 2001 / Accepted: 4 October 2001 / Published online: 20 December 2001     

Transformations RS42(3) of the Ranks ≤ 4¶and Algebraic Solutions of the Sixth Painlevé Equation

Compositions of rational transformations of independent variables of linear matrix ordinary differential equations (ODEs) with the Schlesinger transformations (RS-transformations) are used to construct algebraic solutions of the sixth Painlevé equation. RS-Transformations of the ranks 3 and 4 of 2 × 2 matrix Fuchsian ODEs with 3 singular points into analogous ODE with 4 singular points are classified. Received: 17 August 2001 / Accepted: 14 February 2002     

X-ray-induced photochromic effects in copper-doped lithium niobate crystals

X-Ray-induced absorption changes in Cu-doped lithium niobate crystals (LiNbO₃) are investigated. All induced photochromic effects are fully reversible, i.e., illumination with white light annihilates the absorption changes. With increasing doping level, a decrease in the saturation value of the absorption changes is found. Changes of the Li concentration of the crystal to a more stoichiometric composition via Li indiffusion further decreases the photochromic effect. For sufficient X-ray doses, the saturation value is independent of the radiation energy in the measured range from 50–150 kV. The spectral distribution of the X-ray-induced absorption changes and the slow dark decay indicate that the additional absorption results from an increase of the Cu⁺ concentration. Received: 20 December 2000 / Revised version: 24 January 2001 / Published online: 27 April 2001