Lattice approaches to dilute Fermi gases: Legacy of broken Galilean invariance

In the dilute limit, the properties of fermionic lattice models with short-range attractive interactions converge to those of a dilute Fermi gas in continuum space. We investigate this connection using mean-field and we show that the existence of a finite lattice spacing has consequences down to very small densities. In particular we show that the reduced translational invariance associated to the lattice periodicity has a pivotal role in the finite-density corrections to the universal zero-density limit. For a parabolic dispersion with a sharp cut-off, we provide an analytical expression for the leading-order corrections in the whole BCS-BEC crossover. These corrections, which stem only from the unavoidable cut-off, contribute to the leading-order corrections to the relevant observables. In a generic lattice we find a universal power-law behavior $n^{1/3}$ which leads to significant corrections already for small densities. Our results pose strong constraints on lattice extrapolations of dilute Fermi gas properties.Comment: 10 pages, 7 figure

A darkless space-time

In cosmology it has become usual to introduce new entities as dark matter and dark energy in order to explain otherwise unexplained observational facts. Here, we propose a different approach treating spacetime as a continuum endowed with properties similar to the ones of ordinary material continua, such as internal viscosity and strain distributions originated by defects in the texture. A Lagrangian modeled on the one valid for simple dissipative phenomena in fluids is built and used for empty spacetime. The internal "viscosity" is shown to correspond to a four-vector field. The vector field is shown to be connected with the displacement vector field induced by a point defect in a four-dimensional continuum. Using the known symmetry of the universe, assuming the vector field to be divergenceless and solving the corresponding Euler-Lagrange equation, we directly obtain inflation and a phase of accelerated expansion of spacetime. The only parameter in the theory is the "strength" of the defect. We show that it is possible to fix it in such a way to also quantitatively reproduce the acceleration of the universe. We have finally verified that the addition of ordinary matter does not change the general behaviour of the model.Comment: 13 pages, 7 figures Typos; section V on Newtonian limit adde

Cluster Dynamical Mean-Field Methods for d-wave Superconductors: the Role of Geometry

We compare the accuracy of two cluster extensions of Dynamical Mean-Field Theory in describing d-wave superconductors, using as a reference model a saddle-point t-J model which can be solved exactly in the thermodynamic limit and at the same time reasonably describes the properties of high-temperature superconductors. The two methods are Cellular Dynamical Mean-Field Theory, which is based on a real-space perspective, and Dynamical Cluster Approximation, which enforces a momentum-space picture by imposing periodic boundary conditions on the cluster, as opposed to the open boundary conditions of the first method. We consider the scaling of the methods for large cluster size, but we also focus on the behavior for small clusters, such as those accessible by means of present techniques, with particular emphasis on the geometrical structure, which is definitely a relevant issue in small clusters.Comment: 11 pages, 10 figure

Rotationally-invariant slave-bosons for Strongly Correlated Superconductors

We extend the rotationally invariant formulation of the slave-boson method to superconducting states. This generalization, building on the recent work by Lechermann et al. [Phys. Rev. B {\bf 76}, 155102 (2007)], allows to study superconductivity in strongly correlated systems. We apply the formalism to a specific case of strongly correlated superconductivity, as that found in a multi-orbital Hubbard model for alkali-doped fullerides, where the superconducting pairing has phonic origin, yet it has been shown to be favored by strong correlation owing to the symmetry of the interaction. The method allows to treat on the same footing the strong correlation effects and the interorbital interactions driving superconductivity, and to capture the physics of strongly correlated superconductivity, in which the proximity to a Mott transition favors the superconducting phenomenon.Comment: 18 pages, 7 figure

Finite-density corrections to the Unitary Fermi gas: A lattice perspective from Dynamical Mean-Field Theory

We investigate the approach to the universal regime of the dilute unitary Fermi gas as the density is reduced to zero in a lattice model. To this end we study the chemical potential, superfluid order parameter and internal energy of the attractive Hubbard model in three different lattices with densities of states (DOS) which share the same low-energy behavior of fermions in three-dimensional free space: a cubic lattice, a "Bethe lattice" with a semicircular DOS, and a "lattice gas" with parabolic dispersion and a sharp energy cut-off that ensures the normalization of the DOS. The model is solved using Dynamical Mean-Field Theory, that treats directly the thermodynamic limit and arbitrarily low densities, eliminating finite-size effects. At densities of the order of one fermion per site the lattice and its specific form dominate the results. The evolution to the low-density limit is smooth and it does not allow to define an unambiguous low-density regime. Such finite-density effects are significantly reduced using the lattice gas, and they are maximal for the three-dimensional cubic lattice. Even though dynamical mean-field theory is bound to reduce to the more standard static mean field in the limit of zero density due to the local nature of the self-energy and of the vertex functions, it compares well with accurate Monte Carlo simulations down to the lowest densities accessible to the latter.Comment: 9 pages, 8 figure

Aerodynamic Characteristics of a Supersonic Fighter Aircraft Model at Mach 0.40 to 2.47

The aerodynamic characteristics of an advanced twin-engine fighter aircraft designed for supersonic cruise have been studied in the Langley 16-Foot Transonic Tunnel and the Lewis 10- by 10-Foot Supersonic Tunnel. The objective of this investigation was to establish an aerodynamic data base for the configuration with flow-through nacelles and representative inlets. The use of a canard for trim and the effects of fairing over the inlets were assessed. Comparisons between experimental and theoretical results were also made. The theoretical results were determined by using a potential vortex lift code for subsonic speeds and a linear aerodynamic code for supersonic speeds. This investigation was conducted at Mach numbers from 0.40 to 2.47, at angles of attack from 0 deg to about 20 deg, and at inlet capture ratios of about 0.5 to 1.4

Signature of antiferromagnetic long-range order in the optical spectrum of strongly correlated electron systems

We show how the onset of a non-Slater antiferromagnetic ordering in a correlated material can be detected by optical spectroscopy. Using dynamical mean-field theory we identify two distinctive features: The antiferromagnetic ordering is associated with an enhanced spectral weight above the optical gap, and well separated spin-polaron peaks emerge in the optical spectrum. Both features are indeed observed in LaSrMnO_4 [G\"ossling et al., Phys. Rev. B 77, 035109 (2008)]Comment: 11 pages, 9 figure

Effect of simulated in-flight thrust reversing on vertical-tail loads of F-18 and F-15 airplane models

Investigations were conducted in the Langley 16-Foot Transonic Tunnel to provide data on a 0.10-scale model of the prototype F-18 airplane and a 0.047-scale model of the F-15 three-surface configuration (canard, wing, and horizontal tails). Test data were obtained at static conditions and at Mach numbers from 0.6 to 1.2 over an angle-of-attack range from 2 deg to 15 deg. Nozzle pressure ratio was varied from jet off to about 8.0

Spinoffs and parents in clusters: evidence from the Italian motorcycle industry

In this paper, we study the relation between parenting events and the performance of firms. Using data from the Italian motorcycle industry (1893–1993), we find that parents have higher survival chances after generating a spinoff (i.e. parenting event), confirming results from previous studies about other manufacturing industries. We also show that the survival patterns of parent firms differ across space, and we link them to cluster characteristics: parenting events are associated to survival advantages in the clusters of Milan and the Motorvalley, and to survival disadvantages in the cluster of Turin. The paper contributes to the literature on spinoffs and employee mobility and adds to the debate on the role of clusters and their institutions in evolutionary economic geography, by highlighting the importance of contextual factors for the performance of parent firms