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

Optimized tracking of RF carriers with phase noise, including Pioneer 10 results

The ability to track very weak signals from distant spacecraft is limited by the phase instabilities of the received signal and of the local oscillator employed by the receiver. These instabilities ultimately limit the minimum loop bandwidth that can be used in a phase-coherent receiver, and hence limit the ratio of received carrier power to noise spectral density which can be tracked phase coherently. A method is presented for near real time estimation of the received carrier phase and additive noise spectrum, and optimization of the phase locked loop bandwidth. The method was used with the breadboard Deep Space Network (DSN) Advanced Receiver to optimize tracking of very weak signals from the Pioneer 10 spacecraft, which is now more distant that the edge of the solar system. Tracking with bandwidths of 0.1 Hz to 1.0 Hz reduces tracking signal threshold and increases carrier loop signal to noise ratio (SNR) by 5 dB to 15 dB compared to the 3 Hz bandwidth of the receivers now used operationally in the DSN. This will enable the DSN to track Pioneer 10 until its power sources fails near the end of the century

Resonant tunneling through a small quantum dot coupled to superconducting leads

We address the problem of non-linear transport through discrete electronic levels in a small quantum dot coupled to superconducting electrodes. In our approach the low temperature I-V characteristics can be calculated including all multiple quasi-particle and Andreev processes. The limit of very weak coupling to the leads and large charging energies is briefly analyzed comparing the calculated lineshapes of the I-V curves with recent experimental results. When the coupling to the leads increases and Coulomb blockade effects can be neglected, the combination of multiple Andreev processes and resonant transmission gives rise to a rich subgap structure which largely differs from the one found in the more studied S-N-S systems. We show how multiple processes can be included within a simple sequential tunneling picture qualitatively explaining the subgap structure. We suggest an experimental set-up where the predicted effects could be observed.Comment: 11 pages, 4 postscript figures, to be published in Phys. Rev. B (rapid communications

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

Anomalous Fermi Liquid Behavior of Overdoped High-Tc Superconductors

According to a generic temperature vs. carrier-doping (T-p) phase diagram of high-temperature superconductors it has been proposed that as doping increases to the overdoped region they approach gradually a conventional (canonical) Fermi Liquid. However, Hall effect measurements in several systems reported by different authors show a still strong \emph{T}-dependence in overdoped samples. We report here electrical transport measurements of Y_{1-x}Ca_{x}Ba_{2}Cu_{3}O_{7-delta} thin films presenting a temperature dependence of the Hall constant, R_H, which does not present a gradual transition towards the T-independent behavior of a canonical Fermi Liquid. Instead, the T-dependence passes by a minimum near optimal doping and then increases again in the overdoped region. We discuss the theoretical predictions from two representative Fermi Liquid models and show that they can not give a satisfactory explanation to our data. We conclude that this region of the phase diagram in YBCO, as in most HTSC, is not a canonical Fermi Liquid, therefore we call it Anomalous Fermi Liquid.Comment: 9 pages, 12 figures, to be published in Phys. Rev.

Attractions between charged colloids at water interfaces

The effective potential between charged colloids trapped at water interfaces is analyzed. It consists of a repulsive electrostatic and an attractive capillary part which asymptotically both show dipole--like behavior. For sufficiently large colloid charges, the capillary attraction dominates at large separations. The total effective potential exhibits a minimum at intermediate separations if the Debye screening length of water and the colloid radius are of comparable size.Comment: 8 pages, 1 figure, revised version (one paragraph added) accepted in JPC

Orbital magnetization and its effects in spin-chiral ferromagnetic Kagome lattice

Recently, Berry phase in the semiclassical dynamical of Bloch electrons has been found to make a correction to the phase-space density of states and a general multi-band formula for finite-temperature orbital magnetization has been given [Phys. Rev. Lett. \textbf{97}, 026603 (2006)], where the orbital magnetization $\mathcal{M}$ consists of two parts, i.e., the conventional part $M_{c}$ and the Berry-phase correction part $M_{\Omega}$. Using this general formula, we theoretically investigate the orbital magnetization and its effects on thermoelectric transport and magnetic susceptibility properties of the two-dimensional \textit{kagom\'{e}} lattice with spin anisotropies included. The study in this paper is highly interesting by the occurrence of nonzero Chern number in the lattice. The spin chirality parameter $\phi$ (see text) results in profound effects on the orbital magnetization properties. It is found that the two parts in orbital magnetization opposite each other. In particular, we show that $M_{c}$ and $M_{\Omega}$ yield the paramagnetic and diamagnetic responses, respectively. It is further shown that the orbital magnetization displays fully different behavior in the metallic and insulating regions, which is due to the different roles $M_{c}$ and $M_{\Omega}$ play in these two regions. The anomalous Nernst conductivity is also calculated, which displays a peak-valley structure as a function of the electron Fermi energy.Comment: 9 pages, 7 figure

Running coupling expansion for the renormalized ϕ44\phi^4_4-trajectory from renormalization invariance

We formulate a renormalized running coupling expansion for the $\beta$--function and the potential of the renormalized $\phi^4$--trajectory on four dimensional Euclidean space-time. Renormalization invariance is used as a first principle. No reference is made to bare quantities. The expansion is proved to be finite to all orders of perturbation theory. The proof includes a large momentum bound on the connected free propagator amputated vertices.Comment: 14 pages LaTeX2e, typos and references correcte

Berry's phase contribution to the anomalous Hall effect of gadolinium

When conduction electrons are forced to follow the local spin texture, the resulting Berry phase can induce an anomalous Hall effect (AHE). In gadolinium, as in double-exchange magnets, the exchange interaction is mediated by the conduction electrons and the AHE may therefore resemble that of chromium dioxide and other metallic double-exchange ferromagnets. The Hall resistivity, magnetoresistance, and magnetization of single crystal gadolinium were measured in fields up to 30 T. Measurements between 2 K and 400 K are consistent with previously reported data. A scaling analysis for the Hall resistivity as a function of the magnetization suggests the presence of a Berry's-phase contribution to the anomalous Hall effect.Comment: 6 pages, 7 figures, submitted to Phys. Rev.

A precursor state to unconventional superconductivity in CeIrIn5{_5}

We present sensitive measurements of the Hall effect and magnetoresistance in CeIrIn${_5}$ down to temperatures of 50 mK and magnetic fields up to 15 T. The presence of a low temperature coherent Kondo state is established. Deviations from Kohler's rule and a quadratic temperature dependence of the cotangent of the Hall angle are reminiscent of properties observed in the high temperature superconducting cuprates. The most striking observation pertains to the presence of a \textit{precursor} state--characterized by a change in the Hall mobility--that appears to precede the superconductivity in this material, in similarity to the pseudogap in the cuprate high $T_c$ superconductors.Comment: 4 figure