Dual-species quantum degeneracy of potassium-40 and rubidium-87 on an atom chip

In this article we review our recent experiments with a 40K-87Rb mixture. We demonstrate rapid sympathetic cooling of a 40K-87Rb mixture to dual quantum degeneracy on an atom chip. We also provide details on efficient BEC production, species-selective magnetic confinement, and progress toward integration of an optical lattice with an atom chip. The efficiency of our evaporation allows us to reach dual degeneracy after just 6 s of evaporation - more rapidly than in conventional magnetic traps. When optimizing evaporative cooling for efficient evaporation of 87Rb alone we achieve BEC after just 4 s of evaporation and an 8 s total cycle time.Comment: 8 pages, 4 figures. To be published in the Proceedings of the 20th International Conference on Atomic Physics, 2006 (Innsbruck, Austria

A homomorphism between link and XXZ modules over the periodic Temperley-Lieb algebra

We study finite loop models on a lattice wrapped around a cylinder. A section of the cylinder has N sites. We use a family of link modules over the periodic Temperley-Lieb algebra EPTL_N(\beta, \alpha) introduced by Martin and Saleur, and Graham and Lehrer. These are labeled by the numbers of sites N and of defects d, and extend the standard modules of the original Temperley-Lieb algebra. Beside the defining parameters \beta=u^2+u^{-2} with u=e^{i\lambda/2} (weight of contractible loops) and \alpha (weight of non-contractible loops), this family also depends on a twist parameter v that keeps track of how the defects wind around the cylinder. The transfer matrix T_N(\lambda, \nu) depends on the anisotropy \nu and the spectral parameter \lambda that fixes the model. (The thermodynamic limit of T_N is believed to describe a conformal field theory of central charge c=1-6\lambda^2/(\pi(\lambda-\pi)).) The family of periodic XXZ Hamiltonians is extended to depend on this new parameter v and the relationship between this family and the loop models is established. The Gram determinant for the natural bilinear form on these link modules is shown to factorize in terms of an intertwiner i_N^d between these link representations and the eigenspaces of S^z of the XXZ models. This map is shown to be an isomorphism for generic values of u and v and the critical curves in the plane of these parameters for which i_N^d fails to be an isomorphism are given.Comment: Replacement of "The Gram matrix as a connection between periodic loop models and XXZ Hamiltonians", 31 page

Remarks on the extension of the Ricci flow

We present two new conditions to extend the Ricci flow on a compact manifold over a finite time, which are improvements of some known extension theorems.Comment: 9 pages, to appear in Journal of Geometric Analysi

The one-dimensional Keller-Segel model with fractional diffusion of cells

We investigate the one-dimensional Keller-Segel model where the diffusion is replaced by a non-local operator, namely the fractional diffusion with exponent $0<\alpha\leq 2$. We prove some features related to the classical two-dimensional Keller-Segel system: blow-up may or may not occur depending on the initial data. More precisely a singularity appears in finite time when $\alpha<1$ and the initial configuration of cells is sufficiently concentrated. On the opposite, global existence holds true for $\alpha\leq1$ if the initial density is small enough in the sense of the $L^{1/\alpha}$ norm.Comment: 12 page

Interlayer Quasiparticle Transport in the Vortex State of Josephson Coupled Superconductors

We calculate the dependence of the interlayer quasiparticle conductivity, $\sigma_q$, in a Josephson coupled d-wave superconductor on the magnetic field B||c and the temperature T. We consider a clean superconductor with resonant impurity scattering and a dominant coherent interlayer tunneling. When pancake vortices in adjacent layers are weakly correlated at low T the conductivity increases sharply with B before reaching an extended region of slow linear growth, while at high T it initially decreases and then reaches the same linear regime. For correlated pancakes $\sigma_q$ increases much more strongly with the applied field.Comment: 4 pages, 3 figure

Regularization of Linear Ill-posed Problems by the Augmented Lagrangian Method and Variational Inequalities

We study the application of the Augmented Lagrangian Method to the solution of linear ill-posed problems. Previously, linear convergence rates with respect to the Bregman distance have been derived under the classical assumption of a standard source condition. Using the method of variational inequalities, we extend these results in this paper to convergence rates of lower order, both for the case of an a priori parameter choice and an a posteriori choice based on Morozov's discrepancy principle. In addition, our approach allows the derivation of convergence rates with respect to distance measures different from the Bregman distance. As a particular application, we consider sparsity promoting regularization, where we derive a range of convergence rates with respect to the norm under the assumption of restricted injectivity in conjunction with generalized source conditions of H\"older type

SLE local martingales in logarithmic representations

A space of local martingales of SLE type growth processes forms a representation of Virasoro algebra, but apart from a few simplest cases not much is known about this representation. The purpose of this article is to exhibit examples of representations where L_0 is not diagonalizable - a phenomenon characteristic of logarithmic conformal field theory. Furthermore, we observe that the local martingales bear a close relation with the fusion product of the boundary changing fields. Our examples reproduce first of all many familiar logarithmic representations at certain rational values of the central charge. In particular we discuss the case of SLE(kappa=6) describing the exploration path in critical percolation, and its relation with the question of operator content of the appropriate conformal field theory of zero central charge. In this case one encounters logarithms in a probabilistically transparent way, through conditioning on a crossing event. But we also observe that some quite natural SLE variants exhibit logarithmic behavior at all values of kappa, thus at all central charges and not only at specific rational values.Comment: 40 pages, 7 figures. v3: completely rewritten, new title, new result

General existence proof for rest frame systems in asymptotically flat space-time

We report a new result on the nice section construction used in the definition of rest frame systems in general relativity. This construction is needed in the study of non trivial gravitational radiating systems. We prove existence, regularity and non-self-crossing property of solutions of the nice section equation for general asymptotically flat space times. This proves a conjecture enunciated in a previous work.Comment: 14 pages, no figures, LaTeX 2

Asymptotic behaviour of random tridiagonal Markov chains in biological applications

Discrete-time discrete-state random Markov chains with a tridiagonal generator are shown to have a random attractor consisting of singleton subsets, essentially a random path, in the simplex of probability vectors. The proof uses the Hilbert projection metric and the fact that the linear cocycle generated by the Markov chain is a uniformly contractive mapping of the positive cone into itself. The proof does not involve probabilistic properties of the sample path and is thus equally valid in the nonautonomous deterministic context of Markov chains with, say, periodically varying transitions probabilities, in which case the attractor is a periodic path.Comment: 13 pages, 22 bibliography references, submitted to DCDS-B, added references and minor correction

A single hollow beam optical trap for cold atoms

We present an optical trap for atoms that we have developed for precision spectroscopy measurements. Cold atoms are captured in a dark region of space inside a blue-detuned hollow laser beam formed by an axicon. We analyze the light potential in a ray optics picture and experimentally demonstrate trapping of laser-cooled metastable xenon atoms.Comment: 12 pages, 8 figure