Monoidal Hom-Hopf algebras

Hom-structures (Lie algebras, algebras, coalgebras, Hopf algebras) have been investigated in the literature recently. We study Hom-structures from the point of view of monoidal categories; in particular, we introduce a symmetric monoidal category such that Hom-algebras coincide with algebras in this monoidal category, and similar properties for coalgebras, Hopf algebras and Lie algebras.Comment: 25 pages; extended version: compared to the version that appeared in Comm. Algebra, the Section Preliminary Results and Remarks 5.1 and 6.1 have been adde

Non-proper helicoid-like limits of closed minimal surfaces in 3-manifolds

We show that there exists a metric with positive scalar curvature on S2xS1 and a sequence of embedded minimal cylinders that converges to a minimal lamination that, in a neighborhood of a strictly stable 2-sphere, is smooth except at two helicoid-like singularities on the 2-sphere. The construction is inspired by a recent example by D. Hoffman and B. White.Comment: 12 pages, 3 figures, replaced because of corrupted fil

Classification of graph C*-algebras with no more than four primitive ideals

We describe the status quo of the classification problem of graph C*-algebras with four primitive ideals or less

Shear-stress controlled dynamics of nematic complex fluids

Based on a mesoscopic theory we investigate the non-equilibrium dynamics of a sheared nematic liquid, with the control parameter being the shear stress $\sigma_{\mathrm{xy}}$ (rather than the usual shear rate, $\dot\gamma$). To this end we supplement the equations of motion for the orientational order parameters by an equation for $\dot\gamma$, which then becomes time-dependent. Shearing the system from an isotropic state, the stress- controlled flow properties turn out to be essentially identical to those at fixed $\dot\gamma$. Pronounced differences when the equilibrium state is nematic. Here, shearing at controlled $\dot\gamma$ yields several non-equilibrium transitions between different dynamic states, including chaotic regimes. The corresponding stress-controlled system has only one transition from a regular periodic into a stationary (shear-aligned) state. The position of this transition in the $\sigma_{\mathrm{xy}}$-$\dot\gamma$ plane turns out to be tunable by the delay time entering our control scheme for $\sigma_{\mathrm{xy}}$. Moreover, a sudden change of the control method can {\it stabilize} the chaotic states appearing at fixed $\dot\gamma$.Comment: 10 pages, 11 figure

On U_q(SU(2))-symmetric Driven Diffusion

We study analytically a model where particles with a hard-core repulsion diffuse on a finite one-dimensional lattice with space-dependent, asymmetric hopping rates. The system dynamics are given by the \mbox{U$_{q}$[SU(2)]}-symmetric Hamiltonian of a generalized anisotropic Heisenberg antiferromagnet. Exploiting this symmetry we derive exact expressions for various correlation functions. We discuss the density profile and the two-point function and compute the correlation length $\xi_s$ as well as the correlation time $\xi_t$. The dynamics of the density and the correlations are shown to be governed by the energy gaps of a one-particle system. For large systems $\xi_s$ and $\xi_t$ depend only on the asymmetry. For small asymmetry one finds $\xi_t \sim \xi_s^2$ indicating a dynamical exponent $z=2$ as for symmetric diffusion.Comment: 10 pages, LATE

Effective Edwards-Wilkinson equation for single-file diffusion

In this work, we present an effective discrete Edwards-Wilkinson equation aimed to describe the single-file diffusion process. The key physical properties of the system are captured defining an effective elasticity, which is proportional to the single particle diffusion coefficient and to the inverse squared mean separation between particles. The effective equation gives a description of single-file diffusion using the global roughness of the system of particles, which presents three characteristic regimes, namely normal diffusion, subdiffusion and saturation, separated by two crossover times. We show how these regimes scale with the parameters of the original system. Additional repulsive interaction terms are also considered and we analyze how the crossover times depend on the intensity of the additional terms. Finally, we show that the roughness distribution can be well characterized by the Edwards-Wilkinson universal form for the different single-file diffusion processes studied here.Comment: 9 pages, 9 figure

Neutrino-less Double Electron Capture - a tool to research for Majorana neutrinos

The possibility to observe the neutrino-less double $\beta$ decay and thus to prove the Majorana nature of neutrino as well as provide a sensitive measure of its mass is a major challenge of to-day's neutrino physics. As an attractive alternative we propose to study the inverse process, the radiative neutrino-less double electron capture $0 \nu 2EC$. The associated monoenergetic photon provides a convenient experimental signature. Other advantages include the favourable ratio of the $0 \nu 2EC$ to the competing $2\nu 2EC$ capture rates and, very importantly, the existence of coincidence trigger to suppress the random background. These advantages partly offset the expected longer lifetimes. Rates for the $0\gamma 2EC$ process are calculated. High Z atoms are strongly favoured. A resonance enhancement of the capture rates is predicted at energy release comparable to the $2P-1S$ atomic level difference. The resonance conditions are likely to be met for decays to excited states in final nuclei. Candidates for such studies are considered. The experimental feasibility is estimated and found highly encouraging.Comment: New figure added, table updated, physical background discusse