9,484 research outputs found
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
(rather than the usual shear rate, ). To
this end we supplement the equations of motion for the orientational order
parameters by an equation for , 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 .
Pronounced differences when the equilibrium state is nematic. Here, shearing at
controlled 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
- plane turns out to be tunable by the delay
time entering our control scheme for . Moreover, a sudden
change of the control method can {\it stabilize} the chaotic states appearing
at fixed .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[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 as well
as the correlation time . 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 and depend only on the asymmetry. For
small asymmetry one finds indicating a dynamical exponent
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 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 . The associated monoenergetic
photon provides a convenient experimental signature. Other advantages include
the favourable ratio of the to the competing 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 process are calculated. High Z atoms are
strongly favoured. A resonance enhancement of the capture rates is predicted at
energy release comparable to the 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
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