Turing degrees of limit sets of cellular automata

Cellular automata are discrete dynamical systems and a model of computation. The limit set of a cellular automaton consists of the configurations having an infinite sequence of preimages. It is well known that these always contain a computable point and that any non-trivial property on them is undecidable. We go one step further in this article by giving a full characterization of the sets of Turing degrees of cellular automata: they are the same as the sets of Turing degrees of effectively closed sets containing a computable point

Superconducting d-wave junctions: The disappearance of the odd ac components

We study voltage-biased superconducting planar d-wave junctions for arbitrary transmission and arbitrary orientation of the order parameters of the superconductors. For a certain orientation of the superconductors the odd ac components disappear, resulting in a doubling of the Josephson frequency. We study the sensitivity of this disappearance to orientation and compare with experiments on grain boundary junctions. We also discuss the possibility of a current flow parallel to the junction.Comment: 5 pages, 3 figure

Ab initio calculation of the anomalous Hall conductivity by Wannier interpolation

The intrinsic anomalous Hall effect in ferromagnets depends on subtle spin-orbit-induced effects in the electronic structure, and recent ab-initio studies found that it was necessary to sample the Brillouin zone at millions of k-points to converge the calculation. We present an efficient first-principles approach for computing the anomalous Hall conductivity. We start out by performing a conventional electronic-structure calculation including spin-orbit coupling on a uniform and relatively coarse k-point mesh. From the resulting Bloch states, maximally-localized Wannier functions are constructed which reproduce the ab-initio states up to the Fermi level. The Hamiltonian and position-operator matrix elements, needed to represent the energy bands and Berry curvatures, are then set up between the Wannier orbitals. This completes the first stage of the calculation, whereby the low-energy ab-initio problem is transformed into an effective tight-binding form. The second stage only involves Fourier transforms and unitary transformations of the small matrices set up in the first stage. With these inexpensive operations, the quantities of interest are interpolated onto a dense k-point mesh and used to evaluate the anomalous Hall conductivity as a Brillouin zone integral. The present scheme, which also avoids the cumbersome summation over all unoccupied states in the Kubo formula, is applied to bcc Fe, giving excellent agreement with conventional, less efficient first-principles calculations. Remarkably, we find that more than 99% of the effect can be recovered by keeping a set of terms depending only on the Hamiltonian matrix elements, not on matrix elements of the position operator.Comment: 16 pages, 7 figure

Anomalous Hall effect in a two-dimensional electron gas with spin-orbit interaction

We discuss the mechanism of anomalous Hall effect related to the contribution of electron states below the Fermi surface (induced by the Berry phase in momentum space). Our main calculations are made within a model of two-dimensional electron gas with spin-orbit interaction of the Rashba type, taking into account the scattering from impurities. We demonstrate that such an "intrinsic" mechanism can dominate but there is a competition with the impurity-scattering mechanism, related to the contribution of states in the vicinity of Fermi surface. We also show that the contribution to the Hall conductivity from electron states close to the Fermi surface has the intrinsic properties as well.Comment: 9 pages, 6 figure

A rigorous real time Feynman Path Integral and Propagator

We will derive a rigorous real time propagator for the Non-relativistic Quantum Mechanic $L^2$ transition probability amplitude and for the Non-relativistic wave function. The propagator will be explicitly given in terms of the time evolution operator. The derivation will be for all self-adjoint nonvector potential Hamiltonians. For systems with potential that carries at most a finite number of singularity and discontinuities, we will show that our propagator can be written in the form of a rigorous real time, time sliced Feynman path integral via improper Riemann integrals. We will also derive the Feynman path integral in Nonstandard Analysis Formulation. Finally, we will compute the propagator for the harmonic oscillator using the Nonstandard Analysis Feynman path integral formuluation; we will compute the propagator without using any knowledge of classical properties of the harmonic oscillator

Nano granular metallic Fe - oxygen deficient TiO2−δ_{2-\delta} composite films: A room temperature, highly carrier polarized magnetic semiconductor

Nano granular metallic iron (Fe) and titanium dioxide (TiO$_{2-\delta}$) were co-deposited on (100) lanthanum aluminate (LaAlO$_3$) substrates in a low oxygen chamber pressure using a pulsed laser ablation deposition (PLD) technique. The co-deposition of Fe and TiO$_2$ resulted in $\approx$ 10 nm metallic Fe spherical grains suspended within a TiO$_{2-\delta}$ matrix. The films show ferromagnetic behavior with a saturation magnetization of 3100 Gauss at room temperature. Our estimate of the saturation magnetization based on the size and distribution of the Fe spheres agreed well with the measured value. The film composite structure was characterized as p-type magnetic semiconductor at 300 K with a carrier density of the order of $10^{22} /{\rm cm^3}$. The hole carriers were excited at the interface between the nano granular Fe and TiO$_{2-\delta}$ matrix similar to holes excited in the metal/n-type semiconductor interface commonly observed in Metal-Oxide-Semiconductor (MOS) devices. From the large anomalous Hall effect directly observed in these films it follows that the holes at the interface were strongly spin polarized. Structure and magneto transport properties suggested that these PLD films have potential nano spintronics applications.Comment: 6 pages in Latex including 8 figure

Spin susceptibilities, spin densities and their connection to spin-currents

We calculate the frequency dependent spin susceptibilities for a two-dimensional electron gas with both Rashba and Dresselhaus spin-orbit interaction. The resonances of the susceptibilities depends on the relative values of the Rashba and Dresselhaus spin-orbit constants, which could be manipulated by gate voltages. We derive exact continuity equations, with source terms, for the spin density and use those to connect the spin current to the spin density. In the free electron model the susceptibilities play a central role in the spin dynamics since both the spin density and the spin current are proportional to them.Comment: 6 pages, revtex4 styl

Thermal Casimir Force between Magnetic Materials

We investigate the Casimir pressure between two parallel plates made of magnetic materials at nonzero temperature. It is shown that for real magnetodielectric materials only the magnetic properties of ferromagnets can influence the Casimir pressure. This influence is accomplished through the contribution of the zero-frequency term of the Lifshitz formula. The possibility of the Casimir repulsion through the vacuum gap is analyzed depending on the model used for the description of the dielectric properties of the metal plates.Comment: 9 pages, 3 figures. Contribution to the Proceedings of QFEXT09, Norman, OK, September 21-25, 200

Anomalous Hall effect in Rashba two-dimensional electron systems based on narrow-band semiconductors: side-jump and skew scattering mechanisms

We employ a helicity-basis kinetic equation approach to investigate the anomalous Hall effect in two-dimensional narrow-band semiconductors considering both Rashba and extrinsic spin-orbit (SO) couplings, as well as a SO coupling directly induced by an external driving electric field. Taking account of long-range electron-impurity scattering up to the second Born approximation, we find that the various components of the anomalous Hall current fit into two classes: (a) side-jump and (b) skew scattering anomalous Hall currents. The side-jump anomalous Hall current involves contributions not only from the extrinsic SO coupling but also from the SO coupling due to the driving electric field. It also contains a component which arises from the Rashba SO coupling and relates to the off-diagonal elements of the helicity-basis distribution function. The skew scattering anomalous Hall effect arises from the anisotropy of the diagonal elements of the distribution function and it is a result of both the Rashba and extrinsic SO interactions. Further, we perform a numerical calculation to study the anomalous Hall effect in a typical InSb/AlInSb quantum well. The dependencies of the side-jump and skew scattering anomalous Hall conductivities on magnetization and on the Rashba SO coupling constant are examined.Comment: 16 pages, 4 figures, accepted for publication in PR

ac Josephson effect in superconducting d-wave junctions

We study theoretically the ac Josephson effect in superconducting planar d-wave junctions. The insulating barrier assumed to be present between the two superconductors may have arbitrary strength. Many properties of this system depend on the orientation of the d-wave superconductor: we calculate the ac components of the Josephson current. In some arrangements there is substantial negative differential conductance due to the presence of mid-gap states. We study how robust these features are to finite temperature and also comment on how the calculated current-voltage curves compare with experiments. For some other configurations (for small barrier strength) we find zero-bias conductance peaks due to multiple Andreev reflections through midgap states. Moreover, the odd ac components are strongly suppressed and even absent in some arrangements. This absence will lead to a doubling of the Josephson frequency. All these features are due to the d-wave order parameter changing sign when rotated $90^{\circ}$. Recently, there have been several theoretical reports on parallel current in the d-wave case for both the stationary Josephson junction and for the normal metal-superconductor junction. Also in our case there may appear current density parallel to the junction, and we present a few examples when this takes place. Finally, we give a fairly complete account of the method used and also discuss how numerical calculations should be performed in order to produce current-voltage curves