Examples of scalar-flat hypersurfaces in Rn+1\mathbb{R}^{n+1}

Given a hypersurface $M$ of null scalar curvature in the unit sphere $\mathbb{S}^n$, $n\ge 4$, such that its second fundamental form has rank greater than 2, we construct a singular scalar-flat hypersurface in \Rr^{n+1} as a normal graph over a truncated cone generated by $M$. Furthermore, this graph is 1-stable if the cone is strictly 1-stable.Comment: Paper accepted to publication in Manuscripta Mathematic

Huge Seebeck coefficients in non-aqueous electrolytes

The Seeebeck coefficients of the non-aqueous electrolytes tetrabutylammonium nitrate, tetraoctylphosphonium bromide and tetradodecylammonium nitrate in 1-octanol, 1-dodecanol and ethylene-glycol are measured in a temperature range from T=30 to T=45 C. The Seebeck coefficient is generally of the order of a few hundreds of microvolts per Kelvin for aqueous solution of inorganic ions. Here we report huge values of 7 mV/K at 0.1M concentration for tetrabutylammonium nitrate in 1-dodecanol. These striking results open the question of unexpectedly large kosmotrope or "structure making" effects of tetraalkylammonium ions on the structure of alcohols.Comment: Submitted to J. Chem. Phy

Thermal diffusion by Brownian motion induced fluid stress

The Ludwig-Soret effect, the migration of a species due to a temperature gradient, has been extensively studied without a complete picture of its cause emerging. Here we investigate the dynamics of DNA and spherical particles sub jected to a thermal gradient using a combination of Brownian dynamics and the lattice Boltzmann method. We observe that the DNA molecules will migrate to colder regions of the channel, an observation also made in the experiments of Duhr, et al[1]. In fact, the thermal diffusion coefficient found agrees quantitatively with the experimental value. We also observe that the thermal diffusion coefficient decreases as the radius of the studied spherical particles increases. Furthermore, we observe that the thermal fluctuations-fluid momentum flux coupling induces a gradient in the stress which leads to thermal migration in both systems.Comment: 6 pages, 5 figue

Majorana Spin Liquids, Topology and Superconductivity in Ladders

We theoretically address spin chain analogs of the Kitaev quantum spin model on the honeycomb lattice. The emergent quantum spin liquid phases or Anderson resonating valence bond (RVB) states can be understood, as an effective model, in terms of p-wave superconductivity and Majorana fermions. We derive a generalized phase diagram for the two-leg ladder system with tunable interaction strengths between chains allowing us to vary the shape of the lattice (from square to honeycomb ribbon or brickwall ladder). We evaluate the winding number associated with possible emergent (topological) gapless modes at the edges. In the Az phase, as a result of the emergent Z2 gauge fields and pi-flux ground state, one may build spin-1/2 (loop) qubit operators by analogy to the toric code. In addition, we show how the intermediate gapless B phase evolves in the generalized ladder model. For the brickwall ladder, the $B$ phase is reduced to one line, which is analyzed through perturbation theory in a rung tensor product states representation and bosonization. Finally, we show that doping with a few holes can result in the formation of hole pairs and leads to a mapping with the Su-Schrieffer-Heeger model in polyacetylene; a superconducting-insulating quantum phase transition for these hole pairs is accessible, as well as related topological properties.Comment: 25 pages, 10 figures, final version - to be published in PR

Multiple time-scale approach for a system of Brownian particles in a non-uniform temperature field

The Smoluchowsky equation for a system of interacting Brownian particles in a temperature gradient is derived from the Kramers equation by means of a multiple time-scale method. The interparticle interactions are assumed to be represented by a mean-field description. We present numerical results that compare well with the theoretical prediction together with an extensive discussion on the prescription of the Langevin equation in overdamped systems.Comment: 8 pages, 2 figure

Vortex dynamics in layered superconductors with correlated defects: influence of interlayer coupling

We report a detailed study of the vortex dynamics and vortex phase diagrams of two amorphous Ta_0.3Ge_0.7/Ge multilayered films with intrinsic coplanar defects, but different interlayer coupling. A pinned Bose-glass phase in the more weakly coupled sample exists only below a cross-over field H* in striking contrast to the strongly coupled film. Above H* the flux lines are thought to break up into pancake vortices and the cross-over field is significantly increased when the field is aligned along the extended defects. The two films show different vortex creep excitations in the Bose-glass phase.Comment: zip file: 1 RevTex, 5 figures (png

Vortex dynamics and states of artificially layered superconducting films with correlated defects

Linear resistances and $IV$-characteristics have been measured over a wide range in the parameter space of the mixed phase of multilayered a-TaGe/Ge films. Three films with varying interlayer coupling and correlated defects oriented at an angle $\approx 25$ from the film normal were investigated. Experimental data were analyzed within vortex glass models and a second order phase transition from a resistive vortex liquid to a pinned glass phase. Various vortex phases including changes from three to two dimensional behavior depending on anisotropy have been identified. Careful analysis of $IV$-characteristics in the glass phases revealed a distinctive $T$ and $H$-dependence of the glass exponent $\mu$. The vortex dynamics in the Bose-glass phase does not follow the predicted behavior for excitations of vortex kinks or loops.Comment: 16 pages, 10 figures, 3 table