Exceptional elliptic curves over quartic fields

We study the number of elliptic curves, up to isomorphism, over a fixed quartic field $K$ having a prescribed torsion group $T$ as a subgroup. Let $T=\Z/m\Z \oplus \Z/n\Z$, where $m|n$, be a torsion group such that the modular curve $X_1(m,n)$ is an elliptic curve. Let $K$ be a number field such that there is a positive and finite number of elliptic curves $E_T$ over $K$ having $T$ as a subgroup. We call such pairs $(E_T, K)$ \emph{exceptional}. It is known that there are only finitely many exceptional pairs when $K$ varies through all quadratic or cubic fields. We prove that when $K$ varies through all quartic fields, there exist infinitely many exceptional pairs when $T=\Z/14\Z$ or $\Z/15\Z$ and finitely many otherwise

Dirac quasiparticles in the mixed state

Energies and wave functions are calculated for d-wave quasiparticles in the mixed state using the formalism of Franz and Tesanovic for the low-lying energy levels. The accuracy of the plane-wave expansion is explored by comparing approximate to exact results for a simplified one-dimensional problem, and the convergence of the plane- wave expansion to the two-dimensional case is studied. The results are used to calculate the low-energy tunneling density of states and the low-temperature specific heat, and these theoretical results are compared to semiclassical treatments and to the available data. Implications for the muon spin resonance measurements of vortex core size are also discussed.Comment: 13 pages, 15 figures, RevTeX. References corrected. A factor of 2 in the results has been corrected, and the conclusions have been update

On the ubiquity of trivial torsion on elliptic curves

The purpose of this paper is to give a "down--to--earth" proof of the well--known fact that a randomly chosen elliptic curve over the rationals is most likely to have trivial torsion

Quasiparticle thermal Hall angle and magnetoconductance in YBa_2Cu_3O_x

We present a way to extract the quasiparticle (qp) thermal conductivity Kappa_e and mean-free-path in YBa_2Cu_3O_x, using the thermal Hall effect and the magnetoconductance of Kappa_e. The results are very consistent with heat capacity experiments. Moreover, we find a simple relation between the thermal Hall angle Theta_Q and the H-dependence of Kappa_e, as well as numerical equality between Theta_Q and the electrical Hall angle. The findings also reveal an anomalously anisotropic scattering process in the normal state.Comment: 4 pages in Tex, 5 figures in EPS; replaced on 5/12/99, minor change

Heat Conduction in κ\kappa-(BEDT-TTF)2_2Cu(NCS)2_2

The first study of thermal conductivity, $\kappa$, in a quasi-two-dimensional organic superconductor of the $\kappa$-(BEDT-TTF)$_2$X family reveals features analogous to those already observed in the cuprates. The onset of superconductivity is associated with a sudden increase in $\kappa$ which can be suppressed by the application of a moderate magnetic field. At low temperatures, a finite linear term - due to a residual electronic contribution- was resolved. The magnitude of this term is close to what is predicted by the theory of transport in unconventional superconductors.Comment: 5 pages, 4 figures include

Magnetic Field Dependence of Electronic Specific Heat in Pr_{1.85} Ce_{0.15} CuO_4

The specific heat of electron-doped Pr_{1.85} Ce_{0.15} CuO_4 single crystals is reported for the temperature range 2 - 10 K and magnetic field range 0 - 10 T. A non-linear magnetic field dependence is observed for the field range 0 - 2 T. Our data supports a model with lines of nodes in the gap function of these superconductors. Theoretical calculations of the electronic specific heat for dirty d-wave, clean d-wave, and s-wave symmetries are compared to our data.Comment: 10 pages Latex and 4 eps figures, submitted to Phys. Rev.

Theory of Scanning Tunneling Spectroscopy of Magnetic-Field-Induced Discrete Nodal States in a D-Wave Superconductor

In the presence of an external magnetic field, the low lying elementary excitations of a d-wave superconductor have quantized energy and their momenta are locked near the node direction. It is argued that these discrete states can most likely be detected by a local probe, such as a scanning tunneling microscope. The low temperature local tunneling conductance on the Wigner-Seitz cell boundaries of the vortex lattice is predicted to show peaks spaced as $\pm \sqrt{n}, n ={0,1,2, ...}$. The $n=0$ peak is anomalous, and it is present only if the superconducting order parameter changes sign at certain points on the Fermi surface. Away from the cell boundary, where the superfluid velocity is nonzero, each peak splits, in general, into four peaks, corresponding to the number of nodes in the order parameter.Comment: RevTeX 3.0, 4 pages, 3 figures (included

Anisotropy of magnetothermal conductivity in Sr2RuO4

The dependence of in-plane and interplane thermal conductivities of Sr2RuO4 on temperature, as well as magnetic field strength and orientation, is reported. We found no notable anisotropy in the thermal conductivity for the magnetic field rotation parallel to the conducting plane in the whole range of experimental temperatures and fields, except in the vicinity of the upper critical field Hc2, where the anisotropy of the Hc2 itself plays a dominant role. This finding imposes strong constraints on the possible models of superconductivity in Sr2RuO4 and supports the existence of a superconducting gap with a line of nodes running orthogonal to the Fermi surface cylinder.Comment: published in Phys. Rev. Lett. 4pages, 4 eps figures, LaTe

Efficacy of essential oil mouthwash with and without alcohol: a 3-Day plaque accumulation model

<p>Abstract</p> <p>Background</p> <p>The aim of this study was to evaluate the antiplaque effect of a new alcohol free essential oil mouthwash with respect to a control of an essential oil with alcohol mouthwash, using an <it>in vivo </it>plaque regrowth model of 3-days.</p> <p>Methods</p> <p>The study was designed as a double-masked, randomized, crossover clinical trial, involving 30 volunteers to compare two different essential oil containing mouthwashes, during a 3-day plaque accumulation model. After receiving a thorough professional prophylaxis at the baseline, over the next 3-days each volunteer refrained from all oral hygiene measures and had two daily rinses with 20 ml of the test mouthwash (alcohol free essential oil) or the control mouthwash (essential oil with alcohol). At the end of the each experimental period, plaque was assessed and the panelists filled out a questionnaire. Each subject underwent a 14 days washout period and there was a second allocation.</p> <p>Results</p> <p>The essential oil mouthwash with ethanol shows a better inhibitory effect of plaque regrowth in 3-days than the mouthwash test with only essential oil in the whole mouth (plaque index = 2.18 against 2.46, respectively, p < 0.05); for the lower jaw (plaque index = 2.28 against 2.57, respectively, p < 0.05); for the upper jaw (plaque index = 2.08 against 2.35, respectively, p < 0.05); for the incisors (plaque index = 1.93 against 2.27, respectively, p < 0.05); and the canines (plaque index = 1.99 against 2.47, respectively, p < 0.05).</p> <p>Conclusion</p> <p>The essential oil containing mouthwash without alcohol seems to have a less inhibiting effect on the plaque regrowth than the traditional alcoholic solution.</p> <p>Trial Registration</p> <p>ClinicalTrials.gov <a href="http://www.clinicaltrials.gov/ct2/show/NCT01411618">NCT01411618</a></p

Quantum generated vortices, dual singular gauge transformation and zero temperature transition from d-wave superconductor to underdoped regime

By extending the original Anderson singular gauge transformation for static vortices to two mutual flux-attaching singular gauge transformations for moving vortices, we derive an effective action describing the zero temperature quantum phase transition from d-wave superconductor to underdoped regime. Neglecting the charge fluctuation first, we find that the mutual statistical interaction is exactly marginal. In the underdoped regime, the quasi-particles are described by 2+1 dimensional QED; in the superconducting regime, they are essentially free. However, putting back the charge fluctuation changes the physical picture dramatically: both the dynamic Doppler shift term and the mutual statistical interaction become {\em irrelevant} short-ranged interactions on both sides of the quantum critical point. There are no spin-charge separation and {\em no} dynamic gapless gauge field in the Cooper-pair picture. The formalism developed at $T=0$ is applied to study thermally generated vortices in the vortex plasma regime near the finite temperature KT transition.Comment: 17 pages, 7 figure