1,248 research outputs found
Polyatomic trilobite Rydberg molecules in a dense random gas
Trilobites are exotic giant dimers with enormous dipole moments. They consist
of a Rydberg atom and a distant ground-state atom bound together by short-range
electron-neutral attraction. We show that highly polar, polyatomic trilobite
states unexpectedly persist and thrive in a dense ultracold gas of randomly
positioned atoms. This is caused by perturbation-induced quantum scarring and
the localization of electron density on randomly occurring atom clusters. At
certain densities these states also mix with a s-state, overcoming selection
rules that hinder the photoassociation of ordinary trilobites
Polyatomic trilobite Rydberg molecules in a dense random gas
Trilobites are exotic giant dimers with enormous dipole moments. They consist
of a Rydberg atom and a distant ground-state atom bound together by short-range
electron-neutral attraction. We show that highly polar, polyatomic trilobite
states unexpectedly persist and thrive in a dense ultracold gas of randomly
positioned atoms. This is caused by perturbation-induced quantum scarring and
the localization of electron density on randomly occurring atom clusters. At
certain densities these states also mix with a s-state, overcoming selection
rules that hinder the photoassociation of ordinary trilobites
Completions, branched covers, Artin groups and singularity theory
We study the curvature of metric spaces and branched covers of Riemannian
manifolds, with applications in topology and algebraic geometry. Here curvature
bounds are expressed in terms of the CAT(k) inequality. We prove a general
CAT(k) extension theorem, giving sufficient conditions on and near the boundary
of a locally CAT(k) metric space for the completion to be CAT(k). We use this
to prove that a branched cover of a complete Riemannian manifold is locally
CAT(k) if and only if all tangent spaces are CAT(0) and the base has sectional
curvature bounded above by k. We also show that the branched cover is a
geodesic space. Using our curvature bound and a local asphericity assumption we
give a sufficient condition for the branched cover to be globally CAT(k) and
the complement of the branch locus to be contractible. We conjecture that the
universal branched cover of complex Euclidean n-space over the mirrors of a
finite Coxeter group is CAT(0). Conditionally on this conjecture, we use our
machinery to prove the Arnol'd-Pham-Thom conjecture on K(pi,1) spaces for Artin
groups. Also conditionally, we prove the asphericity of moduli spaces of amply
lattice-polarized K3 surfaces and of the discriminant complements of all the
unimodal hypersurface singularities in Arnol'd's hierarchy
On complete -arcs
Let be a positive integer and be a prime power. For large finite base
fields , we show that any curve can be used to produce a complete
-arc as long as some generic explicit geometric conditions on the curve are
verified. To show the effectiveness of our theory, we derive complete -arcs
from hyperelliptic curves and from Artin-Schreier curves.Comment: Comments are welcome
Complete (k,3)-arcs from quartic curves
Complete (Formula presented.) -arcs in projective planes over finite fields are the geometric counterpart of linear non-extendible Near MDS codes of length (Formula presented.) and dimension (Formula presented.). A class of infinite families of complete (Formula presented.) -arcs in (Formula presented.) is constructed, for (Formula presented.) a power of an odd prime (Formula presented.). The order of magnitude of (Formula presented.) is smaller than (Formula presented.). This property significantly distinguishes the complete (Formula presented.) -arcs of this paper from the previously known infinite families, whose size differs from (Formula presented.) by at most (Formula presented.)
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