Application of the Exact Muffin-Tin Orbitals Theory: the Spherical Cell Approximation

We present a self-consistent electronic structure calculation method based on the {\it Exact Muffin-Tin Orbitals} (EMTO) Theory developed by O. K. Andersen, O. Jepsen and G. Krier (in {\it Lectures on Methods of Electronic Structure Calculations}, Ed. by V. Kumar, O.K. Andersen, A. Mookerjee, Word Scientific, 1994 pp. 63-124) and O. K. Andersen, C. Arcangeli, R. W. Tank, T. Saha-Dasgupta, G. Krier, O. Jepsen, and I. Dasgupta, (in {\it Mat. Res. Soc. Symp. Proc.} {\bf 491}, 1998 pp. 3-34). The EMTO Theory can be considered as an {\it improved screened} KKR (Korringa-Kohn-Rostoker) method which is able to treat large overlapping potential spheres. Within the present implementation of the EMTO Theory the one electron equations are solved exactly using the Green's function formalism, and the Poisson's equation is solved within the {\it Spherical Cell Approximation} (SCA). To demonstrate the accuracy of the SCA-EMTO method test calculations have been carried out.Comment: 20 pages, 10 figure

Directional correlations in quantum walks with two particles

Quantum walks on a line with a single particle possess a classical analogue. Involving more walkers opens up the possibility of studying collective quantum effects, such as many-particle correlations. In this context, entangled initial states and the indistinguishability of the particles play a role. We consider the directional correlations between two particles performing a quantum walk on a line. For non-interacting particles, we find analytic asymptotic expressions and give the limits of directional correlations. We show that by introducing delta-interaction between the particles, one can exceed the limits for non-interacting particles

Full-revivals in 2-D Quantum Walks

Recurrence of a random walk is described by the Polya number. For quantum walks, recurrence is understood as the return of the walker to the origin, rather than the full-revival of its quantum state. Localization for two dimensional quantum walks is known to exist in the sense of non-vanishing probability distribution in the asymptotic limit. We show on the example of the 2-D Grover walk that one can exploit the effect of localization to construct stationary solutions. Moreover, we find full-revivals of a quantum state with a period of two steps. We prove that there cannot be longer cycles for a four-state quantum walk. Stationary states and revivals result from interference which has no counterpart in classical random walks

Effect of Resonance in Soil-Structure Interaction for Finite Soil Layers

In case of seismic design the deformability of the soil should be considered, which can be performed in several ways. Most of the methods do not take into account the finite dimensions of the soil, which results significantly different behavior than the spring-dashpot systems. For an infinite medium, which is used in many cases, there are no eigenmodes, however in practical applications the soft soil is always bounded by rocks. For these cases the soil has eigenmodes and the resonance may influence considerably the response of the system. This question was investigated numerically by FE calculations, and it was found that in certain cases the resonance, which is neglected in the common design process, may significantly enhance the earthquake loads. In this paper this phenomenon is investigated and the parameter range is defined when this effect must be taken into account

Model of Soil-structure Interaction of Objects Resting on Finite Depth Soil Layers for Seismic Design

In case of seismic design of structures the deformability and damping of the soil should be considered, which can be performed in several ways. The infinite soil half space can be approximated with the cone model, which gives constant values for the spring stiffnesses and dashpot characteristics, and an additional mass element for rocking motion. To approximate the dynamic impedance function of a soil layer more complex models were also applied. Most of the methods do not take into account the finite dimensions of the soil, which results significantly different behavior than spring-dashpot systems. To consider the effect of a finite layer a new simple model based on a physical approach is given for the horizontal excitation of strip foundations. Numerical verification is presented, and the parameter range is determined, where the application of the new model is recommended, since applying a spring-dashpot model results in significant errors

Log Fano varieties over function fields of curves

Consider a smooth log Fano variety over the function field of a curve. Suppose that the boundary has positive normal bundle. Choose an integral model over the curve. Then integral points are Zariski dense, after removing an explicit finite set of points on the base curve.Comment: 18 page

Diffeomorphisms and families of Fourier-Mukai transforms in mirror symmetry

Assuming the standard framework of mirror symmetry, a conjecture is formulated describing how the diffeomorphism group of a Calabi-Yau manifold Y should act by families of Fourier-Mukai transforms over the complex moduli space of the mirror X. The conjecture generalizes a proposal of Kontsevich relating monodromy transformations and self-equivalences. Supporting evidence is given in the case of elliptic curves, lattice-polarized K3 surfaces and Calabi-Yau threefolds. A relation to the global Torelli problem is discussed.Comment: Approx. 20 pages LaTeX. One reference adde

Complete classification of trapping coins for quantum walks on the two-dimensional square lattice

One of the unique features of discrete-time quantum walks is called trapping, meaning the inability of the quantum walker to completely escape from its initial position, although the system is translationally invariant. The effect is dependent on the dimension and the explicit form of the local coin. A four-state discrete-time quantum walk on a square lattice is defined by its unitary coin operator, acting on the four-dimensional coin Hilbert space. The well-known example of the Grover coin leads to a partial trapping, i.e., there exists some escaping initial state for which the probability of staying at the initial position vanishes. On the other hand, some other coins are known to exhibit strong trapping, where such an escaping state does not exist. We present a systematic study of coins leading to trapping, explicitly construct all such coins for discrete-time quantum walks on the two-dimensional square lattice, and classify them according to the structure of the operator and the manifestation of the trapping effect. We distinguish three types of trapping coins exhibiting distinct dynamical properties, as exemplified by the existence or nonexistence of the escaping state and the area covered by the spreading wave packet