A rapidly expanding Bose-Einstein condensate: an expanding universe in the lab

We study the dynamics of a supersonically expanding ring-shaped Bose-Einstein condensate both experimentally and theoretically. The expansion redshifts long-wavelength excitations, as in an expanding universe. After expansion, energy in the radial mode leads to the production of bulk topological excitations -- solitons and vortices -- driving the production of a large number of azimuthal phonons and, at late times, causing stochastic persistent currents. These complex nonlinear dynamics, fueled by the energy stored coherently in one mode, are reminiscent of a type of "preheating" that may have taken place at the end of inflation.Comment: 12 pages, 7 figure

Smoothed Complexity Theory

Smoothed analysis is a new way of analyzing algorithms introduced by Spielman and Teng (J. ACM, 2004). Classical methods like worst-case or average-case analysis have accompanying complexity classes, like P and AvgP, respectively. While worst-case or average-case analysis give us a means to talk about the running time of a particular algorithm, complexity classes allows us to talk about the inherent difficulty of problems. Smoothed analysis is a hybrid of worst-case and average-case analysis and compensates some of their drawbacks. Despite its success for the analysis of single algorithms and problems, there is no embedding of smoothed analysis into computational complexity theory, which is necessary to classify problems according to their intrinsic difficulty. We propose a framework for smoothed complexity theory, define the relevant classes, and prove some first hardness results (of bounded halting and tiling) and tractability results (binary optimization problems, graph coloring, satisfiability). Furthermore, we discuss extensions and shortcomings of our model and relate it to semi-random models.Comment: to be presented at MFCS 201

Soft Magnetorotons and Broken-Symmetry States in Bilayer Quantum Hall Ferromagnets

The recent report on the observation of soft magnetorotons in the dispersion of charge-density excitations across the tunneling gap in coupled bilayers at total Landau level filling factor $\nu_T=1$ is reviewed. The inelastic light scattering experiments take advantage of the breakdown of wave-vector conservation that occurs under resonant excitation. The results offer evidence that in the quantum Hall state there is a roton that softens and sharpens markedly when the phase boundary for transitions to highly-correlated compressible states is approached. These findings are interpreted with Hartree-Fock evaluations of the dynamic structure factor. The model includes the effect of disorder in the breakdown of wave-vector conservation and resonance enhancement profiles within a phenomenological approach. These results link the softening of magnetorotons to enhanced excitonic Coulomb interactions in the ferromagnetic bilayers.Comment: 6 pages, 5 figures; conference: EP2DS-1

Utilising family-based designs for detecting rare variant disease associations.

Rare genetic variants are thought to be important components in the causality of many diseases but discovering these associations is challenging. We demonstrate how best to use family-based designs to improve the power to detect rare variant disease associations. We show that using genetic data from enriched families (those pedigrees with greater than one affected member) increases the power and sensitivity of existing case-control rare variant tests. However, we show that transmission- (or within-family-) based tests do not benefit from this enrichment. This means that, in studies where a limited amount of genotyping is available, choosing a single case from each of many pedigrees has greater power than selecting multiple cases from fewer pedigrees. Finally, we show how a pseudo-case-control design allows a greater range of statistical tests to be applied to family data

Onset of Interlayer Phase Coherence in a Bilayer Two-Dimensional Electron System: Effect of Layer Density Imbalance

Tunneling and Coulomb drag are sensitive probes of spontaneous interlayer phase coherence in bilayer two-dimensional electron systems at total Landau level filling factor $\nu_T = 1$. We find that the phase boundary between the interlayer phase coherent state and the weakly-coupled compressible phase moves to larger layer separations as the electron density distribution in the bilayer is imbalanced. The critical layer separation increases quadratically with layer density difference.Comment: 4 pages, 3 figure