Table of contents

A quantum seal is a way of encoding a message into quantum states, so that anybody may read the message with little error, while authorized verifiers can detect that the seal has been broken. We present a simple extension to the Bechmann–Pasquinucci majority-voting scheme that is impervious to coherent attacks, and further, encompasses sealing quantum messages by means of quantum encryption. The scheme is relatively easy to implement, requiring neither entanglement nor controlled operations during the state preparation, reading or verification stages.

The exact solutions of the two-dimensional Schrödinger equation for the hydrogen-like atoms confined by a potential step are obtained. The eigenvalues can be calculated from the matching condition. We generalize this quantum system to arbitrary dimensional D case.

Matrix representations of Maxwell's equations are very well-known. This is evident from the numerous studies on the close resemblance between the Maxwell equations in spinor form to the Dirac equation. However, all these matrix representations lack an exactness, as they assume the media to be homogeneous or/and time-independent. Moreover the final representation is given in terms of a pair of matrix equations. We present a matrix representation of Maxwell's equations in an inhomogeneous linear medium, in presence of sources. It is shown that such a representation necessarily requires 8 × 8 matrices and an explicit representation for them is presented.

In this paper we give an interpretation of Tsallis' nonextensive statistical mechanics based upon the information-theoretic point of view of Luzzi et al [cond-mat/0306217, cond-mat/0306247, cond-mat/0307325], suggesting Tsallis entropy to be not a fundamental concept but a derived one, stemming from an incomplete knowledge of the system, not taking properly into account its interaction with the environment. This interpretation seems to avoid some problems occurring with the original interpretation of Tsallis statistics.

Relativistic configuration interaction f values have been obtained for 264 transitions between the lowest 12 J = 9/2 and 22 J = 9/2° levels. Length and velocity gauges agree to 3.8% for the in-shell transitions, and 10.0% for the shell jump transitions. Two of the J = 9/2° levels are so nearly degenerate that it was necessary to introduce a semiempirical correction to produce the proper level ordering. Landé g values are calculated for all levels, and a more efficient way of adding magnetic Breit effects to the energy matrix is given.

4f² – 4f5g transitions in Pr XII and Nd XIII spectra excited in laser-produced plasma and low-inductance vacuum spark sources were analyzed in the extreme vacuum ultraviolet region. These transitions were observed for the first time in the Cd I isoelectronic sequence. Thirty two (32) spectral lines have been classified in each spectrum, and 24 levels in Pr XII and 23 levels in Nd XIII out of 28 possible levels of 4f5g configuration have been determined. The level value of the 6s6p ¹P₁ level of Pr XII has been revised from 784690 cm^-1 to 791365 cm^-1 based on the new calculations and measurements. The 5s6p ¹P₁ level in Pr XII was also revised on the basis of new measurements. Semi-empirical Least-Squares-Fitting calculations in the frame of Hartree–Fock technique confirmed the experimentally determined energy structures of 4f5g configuration in Pr XII and Nd XIII.

The spectrum of nickel-like Kr IX excited in a fast capillary discharge and photographed with high resolution in the 300–800 Å wavelength region has been investigated. The analysis has been carried out on a basis of the energy parameter interpolation in the NiI isoelectronic sequence. 115 spectral lines belonging to the 3d⁹4s–3d⁹4p–3d⁹4d–3d⁹4f transitions have been classified for the first time and the complete energy structures of 3d⁹4s, 3d⁹4p, 3d⁹4d and 3d⁹4f configurations have been measured in the Kr IX spectrum. The experimental results have been confirmed by the Generalized Least Squares (GLS) Fitting technique using the spectroscopic data obtained for the Ni-like ions from Ga IV through Cd XXI. GLS predictions for 3d⁹4d and 3d⁹4f energy levels in the Zr XIII – Pd XIX sequence are tabulated.

The magnetic dipole and the electric quadrupole hyperfine splitting in heavy Lilike ions is calculated for the (1s)²2p_1/2 and (1s)²2p_3/2 states. The numerical results include the one-electron contributions as well as the interelectronic-interaction correction of order 1/Z, calculated within a rigorous QED approach. Total hyperfine splitting energies are presented for heavy Li-like ions in the range Z = 49–83.

Titanium spectra recorded in the infrared wavelength region with a Fourier Transform Spectrometer have been analysed, and 572 lines have been identified as transitions of the types 3d–4f, 4d–4f and 4f–5g. 11 lines in the UV region around 2400 Å have been identified as belonging to the 3d³4s a⁵F – 3d²4s(⁴F)4f transition array. 113 levels of the 3d²4s(⁴F)4f, 3d³(⁴F)4f and 3d²4s(⁴F)5g subconfigurations have been established. Also six new 4d levels have been found. The number of known Ti I energy levels has been increased by more than 25% and the number of classified lines by 20%. A parametric study of the 4f and 5g configurations has been performed, showing that the structure is best described by the JK coupling approximation.

We report new, extensive CI calculations of the lifetimes of the 4s4p ^1,3P₁^o levels in Ga II. Relativistic effects are introduced via the Breit–Pauli Hamiltonian. Core polarisation is included by means of explicit CI. We obtain lifetime values of 0.528 ns and 3090 ns for the singlet and triplet levels respectively. Oscillator strengths of a number of other transitions are also reported.

The solution of the Dirac equation for hydrogenic atom in static and uniform magnetic field is obtained in the full four-component form. In a basis of spherical spinors wavefunctions for bound states as linear combinations of exact particular solutions in the form of power series are determined by imposing on every radial function the boundary exponential decay. The accuracy of the ground state energy for low and moderately strong magnetic fields exceeds that of previous fully relativistic calculations. In the limit of low magnetic field the high accurate values of the relativistic energy are used to determine the relativistic corrections to the magnetizability up to 15th order in Z²/c².

We have undertaken a number of experimental studies of the structure of singly ionized boron, B II. Much of this work was initially motivated by a search for the "missing" 2s3s ¹S term. There was a surprising disagreement between theory and experiment for this level. In this context lots of data for B II were collected over the years, from beam-foil experiments, high-resolution spark spectroscopy and theoretical calculations. The new material, which includes more than 80 newly classified (or revised) spectral lines, has now been thoroughly analyzed. This was followed by a critical compilation of all known levels and lines of B II, along with the theoretical interpretation of the levels, classifications of the lines and calculated transition probabilities for most lines.

An accurate knowledge of the Li I 4d–4f energy separation is essential for the determination of electric fields, as is pursued using several modern diagnostic techniques. However, there is a rather large spread in the values of this quantity in the available data sources. We have measured the Li I 4d–4f energy separation using a technique that combines laser-induced-fluorescence with the utilization of collisional excitations. The plasma used for these measurements is laser-produced, which allows for selection of an electron-density range for which line shifts due to the plasma microfields are sufficiently small. An observation of the forbidden 2p–4f line provides the information on the microfields that allows for accounting for the Stark-shifts and evaluating the 4d–4f energy separation in the field–free limit. A comparison of the measured value with a few previous measurements allows for resolving the uncertainties in this quantity.

Steady solitons described by the general higher-order extended Ginzburg–Landau equation with fourth order dispersion are studied in this paper. Conditions of the existence and stability of the model parameters of a general chirped soliton-like pulse are analyzed. Numerical evolution of the pulse's existence and stability are studied under a typical example to verify our analysis.

Properties of slow electromagnetic surface waves propagating across an external magnetic field on the second harmonic of ion cyclotron frequency are studied here in the case of plasma with nonuniform density profile and weak spatial dispersion. These waves are eigen modes of the restricted wave guide structure consisting of semi bounded plasma region, dielectric layer (its thickness can be also equal to zero) and metal wall with conductivity that is much larger than that of the plasma. The structure is immersed into an external steady magnetic field oriented parallel to the plasma interface. Theoretical research into effect of transverse nonuniformity of plasma density on dispersion properties of these surface modes is carried out using a kinetic approach and a set of Maxwell equations for their field. To illustrate the ability of these modes to sustain a gas discharge, the flow of their wave power and the quantity of their power absorbed through collisional and collisionless mechanisms of the power transfer into the discharge are calculated. Comparison of the obtained results with the cases of surface cyclotron waves with other polarization is carried out as well.

Calculations of the coefficients of viscosity and thermal conductivity of lithium, sodium, and potassium gases are performed using accurate potential curves. Comparison with previous calculations and measurements is made, and simple expressions are given for the viscosity and thermal conductivity as functions of temperature.

A numerical and experimental study of the impurity concentration and radiation in the EXTRAP-T2R device is reported. The experimental setup consists of an 8-chord bolometer system providing the plasma radiated power and a vacuum-ultraviolet spectrometer providing information on the plasma impurity content. The plasma emissivity profile as measured by the bolometric system is peaked in the plasma centre. A one dimensional Onion Skin Collisional-Radiative model (OSCR) has been developed to compute the density and radiation distributions of the main impurities. The observed centrally peaked emissivity profile can be reproduced by OSCR simulations only if finite particle confinement time and charge-exchange processes between plasma impurities and neutral hydrogen are taken into account. The neutral hydrogen density profile is computed with a recycling code. Simulations show that recycling on metal first wall such as in EXTRAP-T2R (stainless steel vacuum vessel and molybdenum limiters) is compatible with a rather high neutral hydrogen density in the plasma centre. Assuming an impurity concentration of 10% for oxygen and 3% for carbon compared with the electron density, the OSCR calculation including lines and continuum emission reproduces about 60% of the total radiated power with a similarly centrally peaked emissivity profile. The centrally peaked emissivity profile is due to low ionisation stages and strongly radiating species in the plasma core, mainly O⁴⁺ (Be-like) and C³⁺ Li-like.

Nonlinear plasma screening effects on elastic electron-dust grain collisions are investigated in dusty plasmas. The nonlinear screened interaction is considered to obtain the total interaction potential between the projectile electron and the dust grain. The semiclassical straightline trajectory analysis is applied to the path of the projectile electron in order to investigate the variation of the eikonal phase as functions of the impact parameter, dust charge, collision energy, and Debye length. The result shows that the nonlinear correction effects increase the magnitude of the eikonal phase as well as the total scattering cross section. It is found that the nonlinear effects on the eikonal phase are more significant for small impact parameters and decrease with increasing impact parameter.

Experiments were conducted in a Mach 2.5 wind tunnel to explore the modification effect on the shock wave structure by a plasma spike generated by an on-board 60Hz electric discharge in front of a 60° cone-shaped model, which is used as a shock wave generator. Due to cyclic nature of the generated plasma an unsteady shock motion during one discharge period was observed. The pronounced influence of plasma on the shock structure is clearly demonstrated by the result, at the peak of the discharge, showing a transformation of the shock from a well defined attached shock into a classic highly curved bow shock structure, which also appears in diffused form. Experimental results exclude the heating effect as a possible cause of the observed shock wave modification. A theory using a wedge model as the shock generator is developed to introduce a non-heating mechanism responsible for the observed plasma effect on shock waves. Analysis shows that the plasma spike can effectively deflect the incoming flow before the flow reaches the wedge consequently the shock structure in the interaction region is modified from an oblique one to a slightly curved one. The shock front moves upstream with a larger shock angle, consistent with the experimental results.

It is shown that in a highly collisional plasma, electromagnetic waves can propagate beyond the critical density n_c. When the electromagnetic wave propagates obliquely to the plasma density gradient, there exists a critical angle of incidence, below which there is no reflection. When the incident angle is larger than the critical angle, there are two reflection points. One is at a density lower than 2n_c, corresponding to the EM wave incident from low to high density regions. The other one is at a density higher than 2n_c, corresponding to that from high to low density regions.

Kinetic equations for dusty plasma consisting of electrons, ions and spherical grains of different sizes are formulated with regard to grain charging dynamics and solved in the linear approximation. It is assumed that each grain absorbs all encountering electrons and ions. Obtained solutions are expressed in terms of the transition probabilities describing plasma particle transitions in the phase space taking into account inelastic collisions with grains. Such collisions are determined by the charging cross sections for electrons and ions which in turn depend on the self-consistent grain charge. Dielectric response functions for the dusty plasma under consideration are found and dispersion relations are formulated. We present a detailed numerical analysis of such dispersion relation in the low-frequency domain for dusty plasmas containing of one and two grain species. This analysis requires considerable generalization of the plasma dispersion function due to the dependence of the charging cross sections, and thus the collision frequencies, on the particle velocity. It is shown that the presence of dust influences on the dispersion and damping rate of the ion-acoustic waves.

The effect of ion trapping on the shielding of a charged grain in a dusty plasma is reconsidered. The screening potential is obtained analytically and its relation with that from the standard Debye–Hückel theory as well as some existing theories are compared and clarified.

A formulation is presented to treat the electron–lattice scattering in impure metals. This formulation considers the effect of discrete lattice structure beyond that of nearly free electron approximation. Within the formulation, we examine the consequence of positional shift of impurities from ideal lattice sites. We find that the positional deviation of impurities affects the electron–lattice scattering and enhances it when compared to that in an ideal lattice structure with only substitutional impurities. This finding explains recent experimental observation of enhanced electron–lattice scattering in impure metals.

We investigate both analytically and numerically flux flow resonance of long symmetric one dimensional twofold stack Josephson junction in the presence of time independent and spatially homogeneous magnetic field generating Fiske and Eck steps in the current-voltage characteristic. Numerical analysis shows that an asymmetry in the damping coefficients degrades the steepness of the IV curve which is inconvenient when considering the possibility to use such a system in a practical device. Moreover, the case of a junction subjected to a homogeneous microwave field is investigated. We use a perturbative approach to derive the current-voltage characteristic of the junction, showing the appearance of satellite steps around the main Fiske singularity. As a general trend, we show that when the coupling coefficient between the junctions increases, the frequencies at which singularities occur decrease. Good agreement is found between analytical model and numerical results.