Loading a continuous-wave atom laser by optical pumping techniques

Demonstrating that despite loss processes, Bose-Einstein condensates can be formed in steady state is a prerequisite for obtaining a coherent beam of atoms in a continuous-wave atom laser. In this paper we propose a method for loading atoms into the thermal component of a Bose condensed cloud confined in a magnetic trap. This method is aimed at allowing steady state dynamics to be achieved. The proposed scheme involves loading atoms into the conservative magnetic potential using the spontaneous emission of photons. We show that the probability for the reabsorption of these photons may be small .Comment: 6 pages, 7 figure

Coxeter Complexes and Graph-Associahedra

Given a graph G, we construct a simple, convex polytope whose face poset is based on the connected subgraphs of G. This provides a natural generalization of the Stasheff associahedron and the Bott-Taubes cyclohedron. Moreover, we show that for any simplicial Coxeter system, the minimal blow-ups of its associated Coxeter complex has a tiling by graph-associahedra. The geometric and combinatorial properties of the complex as well as of the polyhedra are given. These spaces are natural generalizations of the Deligne-Knudsen-Mumford compactification of the real moduli space of curves.Comment: 18 pages, 9 figures; revised content and reference

Diagonalizing the genome II: toward possible applications

In a previous paper, we showed that the orientable cover of the moduli space of real genus zero algebraic curves with marked points is a compact aspherical manifold tiled by associahedra, which resolves the singularities of the space of phylogenetic trees. In this draft of a sequel, we construct a related (stacky) resolution of a space of real quadratic forms, and suggest, perhaps without much justification, that systems of oscillators parametrized by such objects may may provide useful models in genomics.Comment: 11 pages, 3 figure