Some new results on an old controversy: is perturbation theory the correct asymptotic expansion in nonabelian models?

Several years ago it was found that perturbation theory for two-dimensional O(N) models depends on boundary conditions even after the infinite volume limit has been taken termwise, provided $N>2$. There ensued a discussion whether the boundary conditions introduced to show this phenomenon were somehow anomalous and there was a class of `reasonable' boundary conditions not suffering from this ambiguity. Here we present the results of some computations that may be interpreted as giving some support for the correctness of perturbation theory with conventional boundary conditions; however the fundamental underlying question of the correctness of perturbation theory in these models and in particular the perturbative $\beta$ function remain challenging problems of mathematical physics.Comment: 4 pages, 3 figure

Measurement of a Mixed Spin Channel Feshbach Resonance in Rubidium 87

We report on the observation of a mixed spin channel Feshbach resonance at the low magnetic field value of (9.09 +/- 0.01) G for a mixture of |2,-1> and |1,+1> states in 87Rb. This mixture is important for applications of multi-component BECs of 87Rb, e.g. in spin mixture physics and for quantum entanglement. Values for position, height and width of the resonance are reported and compared to a recent theoretical calculation of this resonance.Comment: 4 pages, 3 figures minor changes, actualized citation

Bose-Einstein condensation at constant temperature

We present a novel experimental approach to Bose-Einstein condensation by increasing the particle number of the system at almost constant temperature. In particular the emergence of a new condensate is observed in multi-component F=1 spinor condensates of 87-Rb. Furthermore we develop a simple rate-equation model for multi-component BEC thermodynamics at finite temperature which well reproduces the measured effects.Comment: 4 pages, 3 figures, RevTe

Dynamics of F=2 Spinor Bose-Einstein Condensates

We experimentally investigate and analyze the rich dynamics in F=2 spinor Bose-Einstein condensates of Rb87. An interplay between mean-field driven spin dynamics and hyperfine-changing losses in addition to interactions with the thermal component is observed. In particular we measure conversion rates in the range of 10^-12 cm^3/s for spin changing collisions within the F=2 manifold and spin-dependent loss rates in the range of 10^-13 cm^3/s for hyperfine-changing collisions. From our data we observe a polar behavior in the F=2 ground state of Rb87, while we measure the F=1 ground state to be ferromagnetic. Furthermore we see a magnetization for condensates prepared with non-zero total spin.Comment: 4 pages, 2 figures, RevTe

Comment on "Scaling Hypothesis for the Spectral Densities in the Nonlinear Sigma Model"

We comment on the recent paper by Balog and Niedermaier [hep-th/9701156].Comment: 3 page

Discrete Symmetry Enhancement in Nonabelian Models and the Existence of Asymptotic Freedom

We study the universality between a discrete spin model with icosahedral symmetry and the O(3) model in two dimensions. For this purpose we study numerically the renormalized two-point functions of the spin field and the four point coupling constant. We find that those quantities seem to have the same continuum limits in the two models. This has far reaching consequences, because the icosahedron model is not asymptotically free in the sense that the coupling constant proposed by L"uscher, Weisz and Wolff [1] does not approach zero in the short distance limit. By universality this then also applies to the O(3) model, contrary to the predictions of perturbation theory.Comment: 18 pages, 8 figures Color coding in Fig. 5 changed to improve visibilit

The Complex Langevin method: When can it be trusted?

We analyze to what extent the complex Langevin method, which is in principle capable of solving the so-called sign problems, can be considered as reliable. We give a formal derivation of the correctness and then point out various mathematical loopholes. The detailed study of some simple examples leads to practical suggestions about the application of the method.Comment: 14 pages, including several eps figures and tables; clarification and minor corrections added, to appear in PR

Lattice artefacts and the running of the coupling constant

We study the running of the L\"uscher-Weisz-Wolff (LWW) coupling constant in the two dimensional O(3) nonlinear $\sigma$ model. To investigate the continuum limit we refine the lattice spacing from the $1\over 16$ value used by LWW up to $1\over 160$. We find that the lattice artefacts are much larger than estimated by LWW and that most likely the coupling constant runs slower than predicted by perturbation theory. A precise determination of the running in the continuum limit would require a controlled ansatz of extrapolation, which, we argue, is not presently available.Comment: 4 pages, 4 figures. To address the criticism that we are studying a different quantitiy than Luscher, Weisz and Wolff originally did, we introduced a new equation (2), a new paragraph discussing this issue and a new figure comparing the results obtained with our prescription to that obtained with the original one of Luscher, Weisz and Wolf

Microseeding – A Powerful Tool for Crystallizing Proteins Complexed with Hydrolyzable Substrates

Hydrolysis is an often-encountered obstacle in the crystallization of proteins complexed with their substrates. As the duration of the crystallization process, from nucleation to the growth of the crystal to its final size, commonly requires several weeks, non-enzymatic hydrolysis of an “unstable” ligand occurs frequently. In cases where the crystallization conditions exhibit non neutral pH values this hydrolysis phenomenon may be even more pronounced. ChoX, the substrate binding protein of a choline ABC-importer, produced crystals with its substrate acetylcholine after one month. However, these crystals exhibited only choline, an acetylcholine hydrolysis product, in the binding site. To overcome this obstacle we devised a microseeding protocol leading to crystals of ChoX with bound acetylcholine within 24 hours. One drawback we encountered was the high twinning fraction of the crystals, possibly was due to the rapid crystal growth