Nonlinear response and scaling law in the vortex state of d-wave superconductors

We study the field dependence of the quasi-particle density of states, the thermodynamics and the transport properties in the vortex state of d-wave superconductors when a magnetic field is applied perpendicular to the conducting plane, specially for the low field and the low temperature compared to the upper critical field and transition temperature, respectively, $H/H_{c2} \ll 1$ and $T/T_c \ll 1$. Both the superfluid density and the spin susceptibility exhibit the characteristic $\sqrt{H}$-field dependence, while the nuclear spin lattice relaxation rate T$_1^{-1}$ and the thermal conductivity are linear in field $H$. With increasing temperature, these quantities exhibit the scaling behavior in $T/\sqrt{H}$. The present theory applies to 2D $f$-wave superconductor as well; a possible candidate of the superconductivity in Sr$_2$RuO$_4$.Comment: 11 pages, 4 figure

Low-lying excitations around a single vortex in a d-wave superconductor

A full quantum-mechanical treatment of the Bogoliubov-de Gennes equation for a single vortex in a d-wave superconductor is presented. First, we find low-energy states extended in four diagonal directions, which have no counterpart in a vortex of s-wave superconductors. The four-fold symmetry is due to 'quantum effect', which is enhanced when $p_{F}\xi$ is small. Second, for $p_{F}\xi \sim 1$, a peak with a large energy gap $E_{0}\sim \Delta$ is found in the density of states, which is due to the formation of the lowest bound states.Comment: 7pages, Revte

Novel vortex lattice transition in d-wave superconductors

We study the vortex state in a magnetic field parallel to the $c$ axis in the framework of the extended Ginzburg Landau equation. We find the vortex acquires a fourfold modulation proportional to $\cos(4\phi)$ where $\phi$ is the angle ${\bf r}$ makes with the $a$-axis. This term gives rise to an attractive interaction between two vortices when they are aligned parallel to $(1,1,0)$ or $(1,-1,0)$. We predict the first order vortex lattice transition at $B=H_{cr}\sim \kappa^{-1} H_{c2}(t)$ from triangular into the square lattice tilted by $45^\circ$ from the $a$ axis. This gives the critical field $H_{cr}$ a few Tesla for YBCO and Bi2212 monocrystals at low temperatures ($T\leq 10 K$).Comment: 6 pages, 4 figure

Discovery From Non-Parties (Third-Party Discovery) in International Arbitration

International arbitration rules and many arbitration laws usually provide procedures that permit tribunals to order parties to disclose documents and other materials to the other parties.1 More complex are the rules that determine opportunities to obtain discovery from persons that are not party to the arbitration (third-party discovery). This article will review third-party discovery under the Federal Arbitration Act (FAA) and the provisions of the US Code s.1782 that authorise US courts to act in aid of actions before foreign tribunals. Section 1782 has unique interest at this time because it figured prominently in the EU antitrust investigation of Intel that was initiated on request from Advanced Micro Devices (AMD). Early in that investigation, AMD filed a s.1782 request in the US District Court to obtain evidence from US sources for submission to the DG-Competition of the European Commission (EC). This request ultimately led to the Supreme Court’s decision in Intel Corp v Advanced Micro Devices Inc2 which appeared to significantly expand the scope of s.1782. Ironically, after AMD won on key legal issues in the Supreme Court, the District Court on remand exercised its discretion and denied the request for judicial assistance. This paper first describes the FAA non-party discovery rules and the split among the federal appellate courts concerning the authority of arbitrators to order prehearing discovery from non-parties. Next, it provides an analysis of the meaning of the terms “interested party” and “tribunal”—terms that were controversially interpreted by the Supreme Court in Intel and are essential to the application of s.1782. Finally, it discusses the “discretionary” factors used by the federal courts in deciding whether to grant a s.1782 request even when the statutory criteria are met. The opportunity to exercise this discretion seems to rebut the argument that the Supreme Court’s interpretation of s.1782 gives participants before foreign tribunals more discovery rights in the United States than are available to the parties in arbitrations covered by the FAA

Holographic interacting dark energy in the braneworld cosmology

We investigate a model of brane cosmology to find a unified description of the radiation-matter-dark energy universe. It is of the interacting holographic dark energy with a bulk-holographic matter $\chi$. This is a five-dimensional cold dark matter, which plays a role of radiation on the brane. Using the effective equations of state $\omega^{\rm eff}_{\rm \Lambda}$ instead of the native equations of state $\omega_{\rm \Lambda}$, we show that this model cannot accommodate any transition from the dark energy with $\omega^{\rm eff}_{\rm \Lambda}\ge-1$ to the phantom regime $\omega^{\rm eff}_{\rm \Lambda}<-1$. Furthermore, the case of interaction between cold dark matter and five dimensional cold dark matter is considered for completeness. Here we find that the redshift of matter-radiation equality $z_{\rm eq}$ is the same order as $z^{\rm ob}_{\rm eq}=2.4\times10^{4} \Omega_{\rm m}h^2$. Finally, we obtain a general decay rate $\Gamma$ which is suitable for describing all interactions including the interaction between holographic dark energy and cold dark matter.Comment: 17 pages, 4 figure

Tunneling current in triplet f-wave superconductors with horizontal lines of nodes

We calculate the tunneling conductance spectra of a normal-metal/insulator/triplet superconductor using the Blonder-Tinkham-Klapwijk (BTK) formulation. Possible states for the superconductor are considered with horizontal lines of nodes, breaking the time reversal symmetry. These results would be useful to discriminate between pairing states in superonductor Sr$_2$RuO$_4$ and also in UPt$_3$.Comment: 12 pages, 7 figure

A Spectral Line Survey from 138.3 to 150.7 GHZ toward Orion-KL

We present the results of a spectral line survey from 138.3 to 150.7 GHz toward Orion-KL. The observations were made using the 14 m radio telescope of Taeduk Radio Astronomy Observatory. Typical system temperatures were between 500 and 700 K, with the sensitivity between $0.02 - 0.06$ K in units of $\rm T_A^*$. A total of 149 line spectra are detected in this survey. Fifty lines have been previously reported, however we find 99 new detections. Among these new lines, 32 are `unidentified', while 67 are from molecular transitions with known identifications. There is no detection of H or He recombination lines. The identified spectra are from a total of 16 molecular species and their isotopic variants. In the range from 138.3 to 150.7 GHz, the strongest spectral line is the J=3-2 transition of CS molecule, followed by transitions of the $\rm H_2CO$, $\rm CH_3OH$, $\rm CH_3CN$, and $\rm SO_2$. Spectral lines from the large organic molecules such as $\rm CH_3OH$, $\rm CH_3OCH_3$, $\rm HCOOCH_3$, $\rm C_2H_5CN$ and $\rm CH_3CN$ are prominent; with 80 % of the identified lines arising from transitions of these molecules. The rotational temperatures and column densities are derived using the standard rotation diagram analysis for $\rm CH_3OH$ ($\rm ^{13}CH_3OH$), $\rm HCOOCH_3$, $\rm CH_3CN$ and $\rm SO_2$ with $\rm 10\sim 270 K$ and $\rm 0.2\sim 20\times 10^{15} cm^{-2}$. These estimates are fairly comparable to the values for the same molecule in other frequency regions by other studies.Comment: 10 figures, 2 tex files for a manuscript and tables, accepted to Ap