Generation of vortices and observation of Quantum Turbulence in an oscillating Bose-Einstein Condensate

We report on the experimental observation of vortex formation and production of tangled vortex distribution in an atomic BEC of Rb-87 atoms submitted to an external oscillatory perturbation. The oscillatory perturbations start by exciting quadrupolar and scissors modes of the condensate. Then regular vortices are observed finally evolving to a vortex tangle configuration. The vortex tangle is a signature of the presence of a turbulent regime in the cloud. We also show that this turbulent cloud has suppression of the aspect ratio inversion typically observed in quantum degenerate bosonic gases during free expansion.Comment: to appear in JLTP - QFS 200

The one-loop six-dimensional hexagon integral and its relation to MHV amplitudes in N=4 SYM

We provide an analytic formula for the (rescaled) one-loop scalar hexagon integral $\tilde\Phi_6$ with all external legs massless, in terms of classical polylogarithms. We show that this integral is closely connected to two integrals appearing in one- and two-loop amplitudes in planar $\\mathcal{N}=4$ super-Yang-Mills theory, $\Omega^{(1)}$ and $\Omega^{(2)}$. The derivative of $\Omega^{(2)}$ with respect to one of the conformal invariants yields $\tilde\Phi_6$, while another first-order differential operator applied to $\tilde\Phi_6$ yields $\Omega^{(1)}$. We also introduce some kinematic variables that rationalize the arguments of the polylogarithms, making it easy to verify the latter differential equation. We also give a further example of a six-dimensional integral relevant for amplitudes in $\\mathcal{N}=4$ super-Yang-Mills.Comment: 18 pages, 2 figure

Three-vortex configurations in trapped Bose-Einstein condensates

We report on the creation of three-vortex clusters in a $^{87}Rb$ Bose-Einstein condensate by oscillatory excitation of the condensate. This procedure can create vortices of both circulation, so that we are able to create several types of vortex clusters using the same mechanism. The three-vortex configurations are dominated by two types, namely, an equilateral-triangle arrangement and a linear arrangement. We interpret these most stable configurations respectively as three vortices with the same circulation, and as a vortex-antivortex-vortex cluster. The linear configurations are very likely the first experimental signatures of predicted stationary vortex clusters.Comment: 4 pages, 4 figure

Amplitudes at Weak Coupling as Polytopes in AdS_5

We show that one-loop scalar box functions can be interpreted as volumes of geodesic tetrahedra embedded in a copy of AdS_5 that has dual conformal space-time as boundary. When the tetrahedron is space-like, it lies in a totally geodesic hyperbolic three-space inside AdS_5, with its four vertices on the boundary. It is a classical result that the volume of such a tetrahedron is given by the Bloch-Wigner dilogarithm and this agrees with the standard physics formulae for such box functions. The combinations of box functions that arise in the n-particle one-loop MHV amplitude in N=4 super Yang-Mills correspond to the volume of a three-dimensional polytope without boundary, all of whose vertices are attached to a null polygon (which in other formulations is interpreted as a Wilson loop) at infinity.Comment: 16 pages, 5 figure

Self-similar expansion of the density profile in a turbulent Bose-Einstein condensate

In a recent study we demonstrated the emergence of turbulence in a trapped Bose-Einstein condensate of Rb-87 atoms. An intriguing observation in such a system is the behavior of the turbulent cloud during free expansion.The aspect ratio of the cloud size does not change in the way one would expect for an ordinary non-rotating (vortex-free) condensate. Here we show that the anomalous expansion can be understood, at least qualitatively, in terms of the presence of vorticity distributed throughout the cloud, effectively counteracting the usual reversal of the aspect ratio seen in free time-of-flight expansion of non-rotating condensates.Comment: 8 pages, 4 figure

Hidden Simplicity of Gauge Theory Amplitudes

These notes were given as lectures at the CERN Winter School on Supergravity, Strings and Gauge Theory 2010. We describe the structure of scattering amplitudes in gauge theories, focussing on the maximally supersymmetric theory to highlight the hidden symmetries which appear. Using the BCFW recursion relations we solve for the tree-level S-matrix in N=4 super Yang-Mills theory, and describe how it produces a sum of invariants of a large symmetry algebra. We review amplitudes in the planar theory beyond tree-level, describing the connection between amplitudes and Wilson loops, and discuss the implications of the hidden symmetries.Comment: 46 pages, 15 figures. v2 ref added, typos fixe

Synaptic abnormalities in the infralimbic cortex of a model of congenital depression

Multiple lines of evidence suggest that disturbances in excitatory transmission contribute to depression. Whether these defects involve the number, size, or composition of glutamatergic contacts is unclear. This study used recently introduced procedures for fluorescence deconvolution tomography in a well-studied rat model of congenital depression to characterize excitatory synapses in layer I of infralimbic cortex, a region involved in mood disorders, and of primary somatosensory cortex. Three groups were studied: (1) rats bred for learned helplessness (cLH); (2) rats resistant to learned helplessness (cNLH); and (3) control Sprague Dawley rats. In fields within infralimbic cortex, cLH rats had the same numerical density of synapses, immunolabeled for either the postsynaptic density (PSD) marker PSD95 or the presynaptic protein synaptophysin, as controls. However, PSD95 immunolabeling intensities were substantially lower in cLH rats, as were numerical densities of synapse-sized clusters of the AMPA receptor subunit GluA1. Similar but less pronounced differences (comparable numerical densities but reduced immunolabeling intensity for PSD95) were found in the somatosensory cortex. In contrast, non-helpless rats had 25% more PSDs than either cLH or control rats without any increase in synaptophysin-labeled terminal frequency. Compared with controls, both cLH and cNLH rats had fewer GABAergic contacts. These results indicate that congenital tendencies that increase or decrease depression-like behavior differentially affect excitatory synapses

Basics of Generalized Unitarity

We review generalized unitarity as a means for obtaining loop amplitudes from on-shell tree amplitudes. The method is generally applicable to both supersymmetric and non-supersymmetric amplitudes, including non-planar contributions. Here we focus mainly on N=4 Yang-Mills theory, in the context of on-shell superspaces. Given the need for regularization at loop level, we also review a six-dimensional helicity-based superspace formalism and its application to dimensional and massive regularizations. An important feature of the unitarity method is that it offers a means for carrying over any identified tree-level property of on-shell amplitudes to loop level, though sometimes in a modified form. We illustrate this with examples of dual conformal symmetry and a recently discovered duality between color and kinematics.Comment: 37 pages, 10 figures. Invited review for a special issue of Journal of Physics A devoted to "Scattering Amplitudes in Gauge Theories", R. Roiban(ed), M. Spradlin(ed), A. Volovich(ed