We present a coupled pair approach for studying few-body physics in harmonically trapped ultracold gases. The method is applied to a two-component Fermi system of $N$ particles. A stochastically variational gaussian expansion method is applied, focus
ing on optimization of the two-body correlations present in the strongly interacting, or unitary, limit. The groundstate energy of the four-, six- and eight-body problem with equal spin populations is calculated with high accuracy and minimal computational effort. We also calculate the structural properties of these systems and discuss their implication for the many-body ultracold gas and other few-body calculations.
This paper introduces a theoretical framework for understanding the accumulation of non-Abelian geometric phases in rotating nitrogen-vacancy centers in diamond. Specifically, we consider how degenerate states can be achieved and demonstrate that the
resulting geometric phase for multiple paths is non-Abelian. We find that the non-Abelian nature of the phase is robust to fluctuations in the path and magnetic field. In contrast to previous studies of the accumulation of Abelian geometric phases for nitrogen-vacancy centers under rotation we find that the limiting time-scale is $T_{1}$. As such a non-Abelian geometric phase accumulation in nitrogen-vacancy centers has potential advantages for applications as gyroscopes.
We present vortex solutions for the homogeneous two-dimensional Bose-Einstein condensate featuring dipolar atomic interactions, mapped out as a function of the dipolar interaction strength (relative to the contact interactions) and polarization direc
tion. Stable vortex solutions arise in the regimes where the fully homogeneous system is stable to the phonon or roton instabilities. Close to these instabilities, the vortex profile differs significantly from that of a vortex in a nondipolar quantum gas, developing, for example, density ripples and an anisotropic core. Meanwhile, the vortex itself generates a mesoscopic dipolar potential which, at distance, scales as 1/r^2 and has an angular dependence which mimics the microscopic dipolar interaction.
This article presents studies on low-field electrical conduction in the range 4-to-300 K for a ultrafast material: InGaAs:ErAs grown by molecular beam epitaxy. The unique properties include nano-scale ErAs crystallines in host semiconductor, a deep F
ermi level, and picosecond ultrafast photocarrier recombination. As the temperature drops, the conduction mechanisms are in the sequence of thermal activation, nearest-neighbor hopping, variable-range hopping, and Anderson localization. In the low-temperature limit, finite-conductivity metallic behavior, not insulating, was observed. This unusual conduction behavior is explained with the Abrahams scaling theory.
SDSS J0015+0104 is the lowest metallicity low surface brightness dwarf (LSBD) galaxy known. The oxygen abundance in its HII region SDSS J001520.70+010436.9 (at ~1.5 kpc from the galaxy centre) is 12+log(O/H)=7.07 (Guseva et al.). This galaxy, at the
distance of 28.4 Mpc, appears to reside deeply in the volume devoid of luminous massive galaxies, known as the Eridanus void. SDSS J235437.29-000501.6 is another Eridanus void LSBD galaxy, with parameter 12+log(O/H)=7.36 (also Guseva et al.). We present the results of their HI observations with the Nancay Radio Telescope revealing their high ratios of M(HI)/L_B ~2.3. Based on the Sloan Digital Sky Survey images, we derived for both galaxies their radial surface brightness profiles and the main photometric parameters. Their colours and total magnitudes are used to estimate the galaxy stellar mass and ages. The related gas mass-fractions, f_g ~0.98 and ~0.97, and the extremely low metallicities (much lower than for their more typical counterparts with the same luminosity) indicate their unevolved status. We compare these Eridanus void LSBDs with several extreme LSBD galaxies residing in the nearby Lynx-Cancer void. Based on the combination of all their unusual properties, the two discussed LSBD galaxies are similar to the unusual LSBDs residing in the closer void. This finding presents additional evidence for the existence in voids of a4 figures, sizable fraction of low-mass unevolved galaxies. Their dedicated search might result in the substantial increase of the number of such objects in the local Universe and in the advancement of understanding their nature.
We derive a governing equation for a Kelvin wave supported on a vortex line in a Bose-Einstein condensate, in a rotating cylindrically symmetric parabolic trap. From this solution the Kelvin wave dispersion relation is determined. In the limit of an
oblate trap and in the absence of longitudinal trapping our results are consistent with previous work. We show that the derived Kelvin wave dispersion in the general case is in quantitative agreement with numerical calculations of the Bogoliubov spectrum and offer a significant improvement upon previous analytical work.
The confluence of quantum physics and biology is driving a new generation of quantum-based sensing and imaging technology capable of harnessing the power of quantum effects to provide tools to understand the fundamental processes of life. One of the
most promising systems in this area is the nitrogen-vacancy centre in diamond - a natural spin qubit which remarkably has all the right attributes for nanoscale sensing in ambient biological conditions. Typically the nitrogen-vacancy qubits are fixed in tightly controlled/isolated experimental conditions. In this work quantum control principles of nitrogen-vacancy magnetometry are developed for a randomly diffusing diamond nanocrystal. We find that the accumulation of geometric phases, due to the rotation of the nanodiamond plays a crucial role in the application of a diffusing nanodiamond as a bio-label and magnetometer. Specifically, we show that a freely diffusing nanodiamond can offer real-time information about local magnetic fields and its own rotational behaviour, beyond continuous optically detected magnetic resonance monitoring, in parallel with operation as a fluorescent biomarker.
Quantum graphity offers the intriguing notion that space emerges in the low energy states of the spatial degrees of freedom of a dynamical lattice. Here we investigate metastable domain structures which are likely to exist in the low energy phase of
lattice evolution. Through an annealing process we explore the formation of metastable defects at domain boundaries and the effects of domain structures on the propagation of bosons. We show that these structures should have observable background independent consequences including scattering, double imaging, and gravitational lensing-like effects.
In this paper we investigate an extremal problem on binary phylogenetic trees. Given two such trees $T_1$ and $T_2$, both with leaf-set ${1,2,...,n}$, we are interested in the size of the largest subset $S subseteq {1,2,...,n}$ of leaves in a common
subtree of $T_1$ and $T_2$. We show that any two binary phylogenetic trees have a common subtree on $Omega(sqrt{log{n}})$ leaves, thus improving on the previously known bound of $Omega(loglog n)$ due to M. Steel and L. Szekely. To achieve this improved bound, we first consider two special cases of the problem: when one of the trees is balanced or a caterpillar, we show that the largest common subtree has $Omega(log n)$ leaves. We then handle the general case by proving and applying a Ramsey-type result: that every binary tree contains either a large balanced subtree or a large caterpillar. We also show that there are constants $c, alpha > 0$ such that, when both trees are balanced, they have a common subtree on $c n^alpha$ leaves. We conjecture that it is possible to take $alpha = 1/2$ in the unrooted case, and both $c = 1$ and $alpha = 1/2$ in the rooted case.
We present a current catalog of 21 cm HI line sources extracted from the Arecibo Legacy Fast Arecibo L-band Feed Array (ALFALFA) survey over ~2800 square degrees of sky: the alpha.40 catalog. Covering 40% of the final survey area, the alpha.40 catalo
g contains 15855 sources in the regions 07h30m < R.A. < 16h30m, +04 deg < Dec. < +16 deg and +24 deg < Dec. < +28 deg and 22h < R.A. < 03h, +14 deg < Dec. < +16 deg and +24 deg < Dec. < +32 deg. Of those, 15041 are certainly extragalactic, yielding a source density of 5.3 galaxies per square degree, a factor of 29 improvement over the catalog extracted from the HI Parkes All Sky Survey. In addition to the source centroid positions, HI line flux densities, recessional velocities and line widths, the catalog includes the coordinates of the most probable optical counterpart of each HI line detection, and a separate compilation provides a crossmatch to identifications given in the photometric and spectroscopic catalogs associated with the Sloan Digital Sky Survey Data Release 7. Fewer than 2% of the extragalactic HI line sources cannot be identified with a feasible optical counterpart; some of those may be rare OH megamasers at 0.16 < z < 0.25. A detailed analysis is presented of the completeness, width dependent sensitivity function and bias inherent in the current alpha.40 catalog. The impact of survey selection, distance errors, current volume coverage and local large scale structure on the derivation of the HI mass function is assessed. While alpha.40 does not yet provide a completely representative sampling of cosmological volume, derivations of the HI mass function using future data releases from ALFALFA will further improve both statistical and systematic uncertainties.
