Dynamical mean-field equations for strongly interacting fermionic atoms in a potential trap

We derive a set of dynamical mean-field equations for strongly interacting fermionic atoms in a potential trap across a Feshbach resonance. Our derivation is based on a variational ansatz, which generalizes the crossover wavefunction to the inhomogeneous case, and the assumption that the order parameter is slowly varying over the size of the Cooper pairs. The equations reduce to a generalized time-dependent Gross-Pitaevskii equation on the BEC side of the resonance. We discuss an iterative method to solve these mean-field equations, and present the solution for a harmonic trap as an illustrating example to self-consistently verify the approximations made in our derivation.Comment: replaced with the published versio

Happiness and the Human Development Index : the paradox of Australia

According to the well-being measure known as the U.N. Human Development Index, Australia now ranks 3rd in the world and higher than all other English-speaking nations. This paper questions that assessment. It reviews work on the economics of happiness, considers implications for policymakers, and explores where Australia lies in international subjective well-being rankings. Using new data on approximately 50,000 randomly sampled individuals from 35 nations, the paper shows that Australians have some of the lowest levels of job satisfaction in the world. Moreover, among the sub-sample of English-speaking nations, where a common language should help subjective measures to be reliable, Australia performs poorly on a range of happiness indicators. The paper discusses this paradox. Our purpose is not to reject HDI methods, but rather to argue that much remains to be understood in this area

Ramping fermions in optical lattices across a Feshbach resonance

We study the properties of ultracold Fermi gases in a three-dimensional optical lattice when crossing a Feshbach resonance. By using a zero-temperature formalism, we show that three-body processes are enhanced in a lattice system in comparison to the continuum case. This poses one possible explanation for the short molecule lifetimes found when decreasing the magnetic field across a Feshbach resonance. Effects of finite temperatures on the molecule formation rates are also discussed by computing the fraction of double-occupied sites. Our results show that current experiments are performed at temperatures considerably higher than expected: lower temperatures are required for fermionic systems to be used to simulate quantum Hamiltonians. In addition, by relating the double occupancy of the lattice to the temperature, we provide a means for thermometry in fermionic lattice systems, previously not accessible experimentally. The effects of ramping a filled lowest band across a Feshbach resonance when increasing the magnetic field are also discussed: fermions are lifted into higher bands due to entanglement of Bloch states, in good agreement with recent experiments.Comment: 9 pages, 7 figure

Paired state in an integrable spin-1 boson model

An exactly solvable model describing the low density limit of the spin-1 bosons in a one-dimensional optical lattice is proposed. The exact Bethe ansatz solution shows that the low energy physics of this system is described by a quantum liquid of spin singlet bound pairs. Motivated by the exact results, a mean-field approach to the corresponding three-dimensional system is carried out. Condensation of singlet pairs and coexistence with ordinary Bose-Einstein condensation are predicted.Comment: 6 pages, 1 figure, Revised versio

Equation of state of a superfluid Fermi gas in the BCS-BEC crossover

We present a theory for a superfluid Fermi gas near the BCS-BEC crossover, including pairing fluctuation contributions to the free energy similar to that considered by Nozieres and Schmitt-Rink for the normal phase. In the strong coupling limit, our theory is able to recover the Bogoliubov theory of a weakly interacting Bose gas with a molecular scattering length very close to the known exact result. We compare our results with recent Quantum Monte Carlo simulations both for the ground state and at finite temperature. Excellent agreement is found for all interaction strengths where simulation results are available.Comment: 7 pages, 4 figures, published version in Europhysics Letters, a long preprint with details will appear soo

Quantum limitations on superluminal propagation

Unstable systems such as media with inverted atomic population have been shown to allow the propagation of analytic wavepackets with group velocity faster than that of light, without violating causality. We illuminate the important role played by unstable modes in this propagation, and show that the quantum fluctuations of these modes, and their unitary time evolution, impose severe restrictions on the observation of superluminal phenomena.Comment: RevTeX 4 page

Effective source approach to self-force calculations

Numerical evaluation of the self-force on a point particle is made difficult by the use of delta functions as sources. Recent methods for self-force calculations avoid delta functions altogether, using instead a finite and extended "effective source" for a point particle. We provide a review of the general principles underlying this strategy, using the specific example of a scalar point charge moving in a black hole spacetime. We also report on two new developments: (i) the construction and evaluation of an effective source for a scalar charge moving along a generic orbit of an arbitrary spacetime, and (ii) the successful implementation of hyperboloidal slicing that significantly improves on previous treatments of boundary conditions used for effective-source-based self-force calculations. Finally, we identify some of the key issues related to the effective source approach that will need to be addressed by future work.Comment: Invited review for NRDA/Capra 2010 (Theory Meets Data Analysis at Comparable and Extreme Mass Ratios), Perimeter Institute, June 2010, CQG special issue - 22 pages, 8 figure

The MUSE-Wide Survey: A first catalogue of 831 emission line galaxies

We present a first instalment of the MUSE-Wide survey, covering an area of 22.2 arcmin$^2$ (corresponding to $\sim$20% of the final survey) in the CANDELS/Deep area of the Chandra Deep Field South. We use the MUSE integral field spectrograph at the ESO VLT to conduct a full-area spectroscopic mapping at a depth of 1h exposure time per 1 arcmin$^2$ pointing. We searched for compact emission line objects using our newly developed LSDCat software based on a 3-D matched filtering approach, followed by interactive classification and redshift measurement of the sources. Our catalogue contains 831 distinct emission line galaxies with redshifts ranging from 0.04 to 6. Roughly one third (237) of the emission line sources are Lyman $\alpha$ emitting galaxies with $3 < z < 6$, only four of which had previously measured spectroscopic redshifts. At lower redshifts 351 galaxies are detected primarily by their [OII] emission line ($0.3 \lesssim z \lesssim 1.5$), 189 by their [OIII] line ($0.21 \lesssim z \lesssim 0.85$), and 46 by their H$\alpha$ line ($0.04 \lesssim z \lesssim 0.42$). Comparing our spectroscopic redshifts to photometric redshift estimates from the literature, we find excellent agreement for $z<1.5$ with a median $\Delta z$ of only $\sim 4 \times 10^{-4}$ and an outlier rate of 6%, however a significant systematic offset of $\Delta z = 0.26$ and an outlier rate of 23% for Ly$\alpha$ emitters at $z>3$. Together with the catalogue we also release 1D PSF-weighted extracted spectra and small 3D datacubes centred on each of the 831 sources.Comment: 24 pages, 14 figures, accepted for publication in A&A, data products are available for download from http://muse-vlt.eu/science/muse-wide-survey/ and later via the CD

New dynamics in cerebellar Purkinje cells: torus canards

We describe a transition from bursting to rapid spiking in a reduced mathematical model of a cerebellar Purkinje cell. We perform a slow-fast analysis of the system and find that -- after a saddle node bifurcation of limit cycles -- the full model dynamics follow temporarily a repelling branch of limit cycles. We propose that the system exhibits a dynamical phenomenon new to realistic, biophysical applications: torus canards.Comment: 4 pages; 4 figures (low resolution); updated following peer-review: language and definitions updated, Figures 1 and 4 updated, typos corrected, references added and remove