Near-crater discoloration of white lead in wall paintings during laser induced breakdown spectroscopy analysis

During Laser-Induced Breakdown Spectroscopy (LIBS) analysis of white lead pigment (basic lead carbonate, 2PbCO₃·Pb(OH)₂), used in wall paintings of historical interest, a yellow–brown discoloration has been observed around the crater. This phenomenon faded after a few days exposure under ambient atmosphere. It was established that the mechanism of this discoloration consists in lead oxides (PbO) formation. It was verified by further experiments under argon atmosphere that recombination of lead with oxygen in the plasma plume produces the oxides, which settle around the crater and induce this discoloration. The impact of discoloration on the artwork's aesthetic aspect and the role of atmosphere on discoloration attenuation are discussed. The mechanism is studied on three other pigments (malachite, Prussian blue and ultramarine blue) and threshold for discoloration occurrence is estimated.     

Controlling qubit arrays with anisotropic XXZ Heisenberg interaction by acting on a single qubit

We investigate anisotropic XXZ Heisenberg spin-1 / 2 chains with control fields acting on one of the end spins, with the aim of exploring local quantum control in arrays of interacting qubits. In this work, which uses a recent Lie-algebraic result on the local controllability of spin chains with “always-on” interactions, we determine piecewise-constant control pulses corresponding to optimal fidelities for quantum gates such as spin-flip (NOT), controlled-NOT (CNOT), and square-root-of-SWAP (). We find the minimal times for realizing different gates depending on the anisotropy parameter Δ of the model, showing that the shortest among these gate times are achieved for particular values of Δ larger than unity. To study the influence of possible imperfections in anticipated experimental realizations of qubit arrays, we analyze the robustness of the obtained results for the gate fidelities to random variations in the control-field amplitudes and finite rise time of the pulses. Finally, we discuss the implications of our study for superconducting charge-qubit arrays.     

Classical and Sobolev orthogonality of the nonclassical Jacobi polynomials with parameters \alpha =\beta =-1

In this paper, we consider the second-order differential expression $$\begin{aligned} \ell [y](x)=(1-x^{2})(-(y^{\prime }(x))^{\prime }+k(1-x^{2})^{-1} y(x))\quad (x\in (-1,1)). \end{aligned}$$ This is the Jacobi differential expression with nonclassical parameters $\alpha =\beta =-1$ in contrast to the classical case when $\alpha ,\beta >-1$ . For fixed $k\ge 0$ and appropriate values of the spectral parameter $\lambda ,$ the equation $\ell [y]=\lambda y$ has, as in the classical case, a sequence of (Jacobi) polynomial solutions $\{P_{n}^{(-1,-1)} \}_{n=0}^{\infty }.$ These Jacobi polynomial solutions of degree $\ge 2$ form a complete orthogonal set in the Hilbert space $L^{2}((-1,1);(1-x^{2})^{-1})$ . Unlike the classical situation, every polynomial of degree one is a solution of this eigenvalue equation. Kwon and Littlejohn showed that, by careful selection of this first-degree solution, the set of polynomial solutions of degree $\ge 0$ are orthogonal with respect to a Sobolev inner product. Our main result in this paper is to construct a self-adjoint operator $T$ , generated by $\ell [\cdot ],$ in this Sobolev space that has these Jacobi polynomials as a complete orthogonal set of eigenfunctions. The classical Glazman–Krein–Naimark theory is essential in helping to construct $T$ in this Sobolev space as is the left-definite theory developed by Littlejohn and Wellman.     

Quasiclassical Green’s function approach to mesoscopic superconductivity

Recent experiments on mesoscopic normal metal/superconductor heterostructures resolve properties on length scales and at low temperatures such that the temperature is below the Thouless energyk_BT ≤ E_Th. We describe the properties of these systems within the framework of quasiclassical many-body techniques. Diffusive and ballistic systems are covered, both in equilibrium and nonequilibrium situations. Thereby we demonstrate the common physical basis of various subtopics.     

Partitioned adaptive Runge-Kutta methods for the solution of nonstiff and stiff systems

Summary For the numerical solution of initial value problems of ordinary differential equations partitioned adaptive Runge-Kutta methods are studied. These methods consist of an adaptive Runge-Kutta methods for the treatment of a stiff system and a corresponding explicit Runge-Kutta method for a nonstiff system. First we modify the theory of Butcher series for partitioned adaptive Runge-Kutta methods. We show that for any explicit Runge-Kutta method there exists a translation invariant partitoned adaptive Runge-Kutta method of the same order. Secondly we derive a special translaton invariant partitioned adaptive Runge-Kutta method of order 3. An automatic stiffness detection and a stepsize control basing on Richardson-extrapolation are performed. Extensive tests and comparisons with the partitioned RKF4RW-algorithm from Rentrop [16] and the partitioned algorithm LSODA from Hindmarsh [9] and Petzold [15] show that the partitoned adaptive Runge-Kutta algorithm works reliable and gives good numericals results. Furthermore these tests show that the automatic stiffness detection in this algorithm is effective.     

Spatial transport phase transitions in systems with high polariton densities

The behaviour of high intense laser beams in matter is examined with respect to a possible pattern formation. The latter is thought to be a collective phenomenon. We establish a microscopic transport theory for anharmonically interacting polaritons, which is valid even for regions far from thermal equilibrium. It is shown that then there must necessarily be phase transitions in the space distribution of polaritons as a function of the laser power. Numerical calculations are performed for an ionic crystal. They yield two critical intensitiesI _c1 andI _c2, where qualitative alterations in the spatial distribution are to be expected. We ascribe the transport phase transitions atI _c1 andI _c2 to the formation of large and small scale filaments respectively. The phenomenon appears to be very similar to the Bénard problem.     

Self-Processing,Diffusion-Based Photopolymers for Holographic Applications

The new photopolymers for holographic applications described herein are based on a cross-linked matrix in which the holographic grating is formed by photo-polymerization of guest monomers in an interference pattern of the recording light. Diffusion of monomer, triggered by this photo-polymerization, from the dark to the bright fringes of the interference pattern is the key parameter for creating high modulation in refractive index Δn during hologram recording. This leads to bright visual volume holograms with high diffraction efficiency. The holographic photopolymers are self-processing. After recording the hologram only (incoherent) light exposure is necessary to bleach the final product and fix the hologram. Unlike earlier photopolymers used in holography, these new materials offer the advantages of no chemical or thermal processing combined with low shrinkage and detuning. Additionally, due to good light sensitivity the formation of the holograms is fast and the film obtained after curing is highly transparent, which makes the material suitable for both, reflection and transmission holography.     

Positive cross correlations in a three-terminal quantum dot with ferromagnetic contacts

We study current fluctuations in an interacting three-terminal quantum dot with ferromagnetic leads. For appropriately polarized contacts, the transport through the dot is governed by dynamical spin blockade, i.e., a spin-dependent bunching of tunneling events not present in the paramagnetic case. This leads, for instance, to positive zero-frequency cross correlations of the currents in the output leads even in the absence of spin accumulation on the dot. We include the influence of spin-flip scattering and identify favorable conditions for the experimental observation of this effect with respect to polarization of the contacts and tunneling rates.