SU(N) Fermions in a One-Dimensional Harmonic Trap

We conduct a theoretical study of SU(N) fermions confined by a one-dimensional harmonic potential. Firstly, we introduce a new numerical approach for solving the trapped interacting few-body problem, by which one may obtain accurate energy spectra across the full range of interaction strengths. In the strong-coupling limit, we map the SU(N) Hamiltonian to a spin-chain model. We then show that an existing, extremely accurate ansatz - derived for a Heisenberg SU(2) spin chain - is extendable to these N-component systems. Lastly, we consider balanced SU(N) Fermi gases that have an equal number of particles in each spin state for N=2, 3, 4. In the weak- and strong-coupling regimes, we find that the ground-state energies rapidly converge to their expected values in the thermodynamic limit with increasing atom number. This suggests that the many-body energetics of N-component fermions may be accurately inferred from the corresponding few-body systems of N distinguishable particles.Comment: 15 pages, 6 figure

X-ray properties of UV-selected star forming galaxies at z~1 in the Hubble Deep Field North

We present an analysis of the X-ray emission from a large sample of ultraviolet (UV) selected, star forming galaxies with 0.74<z<1.32 in the Hubble Deep Field North (HDF-N) region. By excluding all sources with significant detected X-ray emission in the 2 Ms Chandra observation we are able to examine the properties of galaxies for which the emission in both UV and X-ray is expected to be predominantly due to star formation. Stacking the X-ray flux from 216 galaxies in the soft and hard bands produces significant detections. The derived mean 2-10 keV rest-frame luminosity is 2.97+/-0.26x10^(40) erg/s, corresponding to an X-ray derived star formation rate (SFR) of 6.0+/-0.6 Msolar/yr. Comparing the X-ray value with the mean UV derived SFR, uncorrected for attenuation, we find that the average UV attenuation correction factor is \~3. By binning the galaxy sample according to UV magnitude and colour, correlations between UV and X-ray emission are also examined. We find a strong positive correlation between X-ray emission and rest-frame UV emission. A correlation between the ratio of X-ray-to-UV emission and UV colour is also seen, such that L(X)/L(UV) increases for redder galaxies. Given that X-ray emission offers a view of star formation regions that is relatively unaffected by extinction, results such as these can be used to evaluate the effects of dust on the UV emission from high-z galaxies. For instance we derive a relationship for estimating UV attenuation corrections as a function of colour excess. The observed relation is inconsistent with the Calzetti et al. (2000) reddening law which over predicts the range in UV attenuation corrections by a factor of ~100 for the UV selected z~1 galaxies in this sample (abridged).Comment: 10 pages, 7 figures, accepted for publication in MNRA

Quantum transport in carbon nanotubes

Carbon nanotubes are a versatile material in which many aspects of condensed matter physics come together. Recent discoveries, enabled by sophisticated fabrication, have uncovered new phenomena that completely change our understanding of transport in these devices, especially the role of the spin and valley degrees of freedom. This review describes the modern understanding of transport through nanotube devices. Unlike conventional semiconductors, electrons in nanotubes have two angular momentum quantum numbers, arising from spin and from valley freedom. We focus on the interplay between the two. In single quantum dots defined in short lengths of nanotube, the energy levels associated with each degree of freedom, and the spin-orbit coupling between them, are revealed by Coulomb blockade spectroscopy. In double quantum dots, the combination of quantum numbers modifies the selection rules of Pauli blockade. This can be exploited to read out spin and valley qubits, and to measure the decay of these states through coupling to nuclear spins and phonons. A second unique property of carbon nanotubes is that the combination of valley freedom and electron-electron interactions in one dimension strongly modifies their transport behaviour. Interaction between electrons inside and outside a quantum dot is manifested in SU(4) Kondo behavior and level renormalization. Interaction within a dot leads to Wigner molecules and more complex correlated states. This review takes an experimental perspective informed by recent advances in theory. As well as the well-understood overall picture, we also state clearly open questions for the field. These advances position nanotubes as a leading system for the study of spin and valley physics in one dimension where electronic disorder and hyperfine interaction can both be reduced to a very low level.Comment: In press at Reviews of Modern Physics. 68 pages, 55 figure

The X-ray luminosity function of AGN at z~3

We combine Lyman-break colour selection with ultradeep (> 200 ks) Chandra X-ray imaging over a survey area of ~0.35 deg^2 to select high redshift AGN. Applying careful corrections for both the optical and X-ray selection functions, the data allow us to make the most accurate determination to date of the faint end of the X-ray luminosity function (XLF) at z~3. Our methodology recovers a number density of X-ray sources at this redshift which is at least as high as previous surveys, demonstrating that it is an effective way of selecting high z AGN. Comparing to results at z=1, we find no evidence that the faint slope of the XLF flattens at high z, but we do find significant (factor ~3.6) negative evolution of the space density of low luminosity AGN. Combining with bright end data from very wide surveys we also see marginal evidence for continued positive evolution of the characteristic break luminosity L*. Our data therefore support models of luminosity-dependent density evolution between z=1 and z=3. A sharp upturn in the the XLF is seen at the very lowest luminosities (Lx < 10^42.5 erg s^-1), most likely due to the contribution of pure X-ray starburst galaxies at very faint fluxes.Comment: 16 pages, 9 figures, accepted for publication in MNRA

Carbon nanotube quantum dots on hexagonal boron nitride

We report the fabrication details and low-temperature characteristics of the first carbon nanotube (CNT) quantum dots on flakes of hexagonal boron nitride (hBN) as substrate. We demonstrate that CNTs can be grown on hBN by standard chemical vapor deposition and that standard scanning electron microscopy imaging and lithography can be employed to fabricate nanoelectronic structures when using optimized parameters. This proof of concept paves the way to more complex devices on hBN, with more predictable and reproducible characteristics and electronic stability.Comment: 4 pages, 4 figure

The X-ray emission of Lyman break galaxies

We present an analysis of the X-ray emission of a large sample of z∼3 Lyman break galaxies (LBGs), based on Chandra/ACIS observations of several LBG survey fields. A total of 24 LBGs are directly detected in the X-ray, approximately doubling the number of known detections. Thirteen of the LBGs have optical spectroscopic signatures of active galactic nucleus (AGN) activity, but almost all the other X-ray detections are also likely to host an accreting black hole based on their X-ray properties. The AGN exhibit a wide range in X-ray luminosity, from weak Seyferts to bright quasi-stellar objects (QSOs). An optical spectroscopy identified approximately one-third of the X-ray-detected sources as broad-line QSOs, one-third as narrow-line AGN (NLAGN) and one-third as normal star-forming LBGs. The fraction of X-ray-detected LBGs is 3 per cent, much lower than that which has been found for submillimetre-selected galaxies. Two galaxies have X-ray luminosities, spectra and fX/fopt values that are consistent with emission from star formation processes and are identified as candidate X-ray bright, pure starburst galaxies at z∼ 3. If powered solely by star formation, the sources would have star formation rates (SFRs) of 300–500 M⊙ yr−1. X-ray spectral analysis of the LBGs shows a mean photon index of Γ= 1.96 , similar to local AGN. There is evidence for absorption in at least 40 per cent of the objects. Significantly more absorption is evident in the NLAGN, which is consistent with AGN unification schemes. After correction for absorption, the narrow- and broad-line objects show the same average luminosity. X-ray-detected LBGs, spectroscopically classified as normal galaxies, however, are less luminous in both soft and hard X-ray bands, indicating that the host galaxy is outshining any optical AGN signature. Turning to the X-ray emission from LBGs without direct detections, stacking the X-ray flux in the two deepest Chandra fields under consideration [the Hubble Deep Field-North (HDF-N) and Groth–Westphal Strip (GWS)] produced significant detections in each, although the GWS result was marginal. The detection in the HDF-N gives an X-ray-derived SFR of 42.4 ± 7.8 M⊙ yr^−1 per LBG and, by comparing with the ultraviolet (UV) SFR, the implied UV extinction correction is 4.1 ± 0.8. The LBG sample was split into three bins based on UV magnitude to examine the correlation between UV and X-ray emission: for the limited statistics available, there was no evidence of any correlation

Frustrated orbital Feshbach resonances in a Fermi gas

The orbital Feshbach resonance (OFR) is a novel scheme for magnetically tuning the interactions in closed-shell fermionic atoms. Remarkably, unlike the Feshbach resonances in alkali atoms, the open and closed channels of the OFR are only very weakly detuned in energy. This leads to a unique effect whereby a medium in the closed channel can Pauli block, or frustrate, the two-body scattering processes. Here, we theoretically investigate the impact of frustration in the few- and many-body limits of the experimentally accessible three-dimensional $^{173}$Yb system. We find that by adding a closed-channel atom to the two-body problem, the binding energy of the ground state is significantly suppressed, and by introducing a closed-channel Fermi sea to the many-body problem, we can drive the system towards weaker fermion pairing. These results are potentially relevant to superconductivity in solid-state multiband materials, as well as to the current and continuing exploration of unconventional Fermi-gas superfluids near the OFR.Comment: 14 pages, 6 figure

Social Assessment of Section 3 of the A465 Heads of the Valleys Road: Brynmawr to Tredegar

The aim of this report is to provide a social assessment of the impacts of Section 3 of the A465 Heads of the Valleys Road: Brynmawr to Tredegar, using a mixed methods approach which adapts and builds on the UK WebTAG appraisal guidance units 4.1 and 4.2. We define social assessment in this document as a study of the social and distributional impacts which estimate the impacts of the implemented scheme at the point of opening rather than a detailed ex-ante appraisal. In the absence of detailed ex-ante appraisal, this report sets a baseline from which future evaluation may be conducted. This is the first application of a new mixed methods approach to social assessment of the impacts of transport infrastructure investment in the UK. It was commissioned by the Welsh Government in specific recognition of the need for improved guidance in this area of project delivery. The results reported here, along with its accompanying annexes, also contribute to greater understanding of social and distributional impacts, which builds upon and extends the current quantitative approach in WelTAG / WebTAG. This will hopefully lead to better understanding of the wider social effects of transport projects in order to inform future considerations as to how new transport schemes affect wellbeing