Abstract: In order to increase the accuracy of the linearized augmented plane wave (LAPW) method, we present a new approach where the plane wave basis function is augmented by two different atomic radial components constructed at two different linearization energies corresponding to two different electron bands (or energy windows). We demonstrate that this case can be reduced to the standard treatment within the LAPW paradigm where the usual basis set is enriched by the basis functions of the tight binding type, which go to zero with zero derivative at the sphere boundary. We show that the task is closely related with the problem of extended core states which is currently solved by applying the LAPW method with local orbitals (LAPW+LO). In comparison with LAPW+LO, the number of supplemented basis functions in our approach is doubled, which opens up a new channel for the extension of the LAPW and LAPW+LO basis sets. The appearance of new supplemented basis functions absent in the LAPW+LO treatment is closely related with the existence of the ul-component in the canonical LAPW method. We discuss properties of additional tight binding basis functions and apply the extended basis set for computation of electron energy bands of lanthanum (face and body centered structures) and hexagonal close packed lattice of cadmium. We demonstrate that the new treatment gives lower total energies in comparison with both canonical LAPW and LAPW+LO, with the energy difference more pronounced for intermediate and poor LAPW basis sets.

Abstract: Dielectric properties of nano-confined water are important in several areas of science, i.e., it is relevant in the dielectric double layer that exists in practically all heterogeneous fluid-based systems. Molecular dynamics simulations are used to predict the in-plane dielectric properties of confined water in planar channels of width ranging from sub-nanometer to bulk. Because of suppressed rotational degrees of freedom near the confining walls, the dipole of the water molecules tends to be aligned parallel to the walls, which results in a strongly enhanced in-plane dielectric constant (epsilon (parallel to)) reaching values of about 120 for channels with height 8 angstrom < h < 10 angstrom. With the increase in the width of the channel, we predict that epsilon (parallel to) decreases nonlinearly and reaches the bulk value for h > 70 angstrom. A stratified continuum model is proposed that reproduces the h > 10 angstrom dependence of epsilon (parallel to). For sub-nanometer height channels, abnormal behavior of epsilon (parallel to) is found with two orders of magnitude reduction of epsilon (parallel to) around h similar to 7.5 angstrom, which is attributed to the formation of a particular ice phase that exhibits long-time (similar to mu s) stable ferroelectricity. This is of particular importance for the understanding of the influence of confined water on the functioning of biological systems.

Abstract: A microscopic theory, which describes the orientational dynamics of C60 molecules in the face-centered cubic phase of C60-fullerite, is formulated or the case of a complex molecular structure. Interaction centers which comprise atoms, double bonds, and single bonds as molecular constituents contribute to the intermolecular potential. Orientation dependent physical properties are described in terms of symmetry-adapted rotator functions. It is found that a same set of rotator functions is sufficient even in the case of a complex molecular structure. Phase transition temperatures are discussed for various models of molecular structure.

Abstract: We numerically study the vortex-vortex interaction in multicomponent homogeneous Bose-Einstein condensates within the realm of the Gross-Pitaevskii theory. We provide strong evidence that pairwise vortex interaction captures the underlying mechanisms which determine the geometric configuration of the vortices, such as different lattices in many-vortex states, as well as the bound vortex states with two (dimer) or three (trimer) vortices. Specifically, we discuss and apply our theoretical approach to investigate intra- and intercomponent vortex-vortex interactions in two- and three-component Bose-Einstein condensates, thereby shedding light on the formation of the exotic vortex configurations. These results correlate with current experimental efforts in multicomponent Bose-Einstein condensates and the understanding of the role of vortex interactions in multiband superconductors.

Abstract: We show numerically that a rotating, harmonically trapped mixture of two Bose-Einstein-condensed superfluids cancontrary to its single-species counterpartcontain a multiply quantized vortex in the ground state of the system. This giant vortex can occur without any accompanying single-quantum vortices, may either be coreless or have an empty core, and can be realized in a Rb87−K41 Bose-Einstein condensate. Our results not only provide a rare example of a stable, solitary multiquantum vortex but also reveal exotic physics stemming from the coexistence of multiple, compositionally distinct condensates in one system.

Abstract: Recent theoretical and experimental developments in the field of electron-vortex-beam physics have raised questions about what exactly this novelty in the field of electron microscopy (and other fields, such as particle physics) really provides. An important part of the answer to these questions lies in scattering theory. The present investigation explores various aspects of inelastic quantum scattering theory for cylindrically symmetric beams with orbital angular momentum. The model system of Coulomb scattering on a hydrogen atom provides the setting to address various open questions: How is momentum transferred? Do vortex beams selectively excite atoms, and how can one employ vortex beams to detect magnetic transitions? The analytical approach presented here provides answers to these questions. OAM transfer is possible, but not through selective excitation; rather, by pre- and postselection one can filter out the relevant contributions to a specific signal.

Abstract: The interaction of a wave packet (and in particular the wave front) with a mass barrier is investigated in one dimension. We discuss the main features of the wave packet that are inherent to two-dimensional wave packets, such as compression during reflection, penetration in the case when the energy is lower than the height of the barrier, waving tails, precursors, and the retardation of the reflected and penetrated wave packets. These features depend on the wave-packet envelope function which we demonstrate by considering the case of a rectangular wave packet with sharp front and trailing edges and a smooth Gaussian wave packet. The method of Fourier integral for obtaining the nonstationary solutions is used.

Abstract: The Higgs amplitude mode of the order parameter of an ultracold confined Fermi gas in the BCS regime after a quench of the coupling constant is analyzed theoretically. A characteristic feature is a damped oscillation which at a certain transition time changes into a rather irregular dynamics. We compare the numerical solution of the full set of nonlinear equations of motion for the normal and anomalous Bogoliubov quasiparticle excitations with a linearized approximation. In doing so the transition time as well as the difference between resonant systems, i.e., systems where the Fermi energy is close to a sub-band minimum, and off-resonant systems can be well understood and traced back to the system and geometry parameters.

Abstract: We show numerically that a harmonically trapped and coherently Rabi-coupled three-component Bose-Einstein condensate can host unconventional vortex lattices in its rotating ground state. The discovered lattices incorporate square and zig-zag patterns, vortex dimers and chains, and doubly quantized vortices, and they can be quantitatively classified in terms of a skyrmionic topological index, which takes into account the multicomponent nature of the system. The exotic ground-state lattices arise due to the intricate interplay of the repulsive density-density interactions and the Rabi couplings as well as the ubiquitous phase frustration between the components. In the frustrated state, domain walls in the relative phases can persist between some components even at strong Rabi coupling, while vanishing between others. Consequently, in this limit the three-component condensate effectively approaches a two-component condensate with only density-density interactions. At intermediate Rabi coupling strengths, however, we face unique vortex physics that occurs neither in the two-component counterpart nor in the purely density-density-coupled three-component system.

Abstract: This study focuses on optimizing the composition and firing temperature of porcelain tiles using statistical analysis techniques. A full factorial design, including model adequacy checking, analysis of variance, Pareto charts, interaction plots, regression model, and response optimizer is employed. The key factors were the Seger ratios of SiO2/Al2O3, Na2O/K2O, MgO/CaO, and firing temperature. The response variables investigated were bulk density, water absorption, linear shrinkage, coefficient of thermal expansion (at 500 degrees C), and strength. The statistical analysis revealed highly significant results, which were further validated, confirming their reliability for practical use in the production of porcelain tiles. The study demonstrated the effectiveness of utilizing Seger formulas and properties of typical raw materials to accurately predict the final properties of ceramic tiles. By employing SiO2/Al2O3 = 5.2, Na2O/K2O = 1.50, MgO/CaO = 3.0, and firing temperature of 1180 degrees C, optimized properties, such as maximum strength, maximum bulk density, and minimum water absorption, was achieved with a composite desirability of 0.9821.

Abstract: Recent advances in manufacturing arrays of artificial pinning sites, i.e., antidots, blind holes and magnetic dots, allowed an effective control of magnetic flux in superconductors. An array of magnetic bars deposited on top of a superconducting film was shown to display different pinning regimes depending on the direction of the in-plane magnetization of the bars. Changing the sign of their magnetization results in changes in the induced magnetic pinning potentials. By numerically solving the time-dependent Ginzburg-Landau equations in a superconducting film with periodic arrays of zigzag-arranged magnetic bars, we revealed various flux dynamics regimes. In particular, we demonstrate flux pinning and flux flow, depending on the direction of the magnetization of the magnetic bars. Remarkably, the revealed different flux-motion regimes are associated with different mechanisms of vortex-antivortex dynamics. For example, we found that for an 'antiparallel' configuration of magnetic bars this dynamics involves a repeating vortex-antivortex generation and annihilation. We show that the depinning transition and the onset of flux flow can be manipulated by the magnetization of the bars and the geometry of the array. This provides an effective control of the depinning critical current that can be useful for possible fluxonics applications.

Abstract: We study vortex configurations in mesoscopic superconducting squares. Our theoretical approach is based on the analytical solution of the London equation using the Green's function method. The potential energy landscape found is then used in Langevin-type molecular-dynamics simulations to obtain stable vortex configurations. We show that the filling rules for vortices in squares with increasing applied magnetic field can be formulated, although in a different manner than in disks, in terms of the formation of vortex 'shells'. We discuss metastable states and the stability of the vortex configurations found with respect to variations of the material parameters and deformations of the shape of the sample.

Abstract: The dynamics of Josephson vortices (fluxons) in artificial stacks of superconducting-normal-superconducting Josephson junctions is investigated using the anisotropic time-dependent Ginzburg-Landau theory in the presence of a square/rectangular array of pinning centers (holes). For small values of the applied drive, fluxons in different junctions move out of phase, forming a periodic triangular lattice. A rectangular lattice of moving fluxons is observed at larger currents, which is in agreement with previous theoretical predictions (Koshelev and Aranson 2000 Phys. Rev. Lett. 85 3938). This 'superradiant' flux-flow state is found to be stable in a wide region of applied current. The stability range of this ordered state is considerably larger than the one obtained for the pinning-free sample. Clear commensurability features are observed in the current-voltage characteristics of the system with pronounced peaks in the critical current at (fractional) matching fields. The effect of density and strength of the pinning centers on the stability of the rectangular fluxon lattice is discussed. Predicted synchronized motion of fluxons in the presence of ordered pinning can be detected experimentally using the rf response of the system, where enhancement of the Shapiro-like steps is expected due to the synchronization.