Photon spheres in Einstein and Einstein-Gauss-Bonnet theories and circular null geodesics in axially-symmetric spacetimes

In this article we extend a recent theorem proven by Hod (Phys. Lett. B, {\bf 727}, 345--348, 2013) to $n$-dimensional Einstein and Einstein-Gauss-Bonnet theories, which gives an upper bound for the photon sphere radii of spherically symmetric black holes. As applications of these results we give a universal upper bound for the real part of quasinormal modes in the WKB limit and a universal lower bound for the position of the first relativistic image in the strong lensing regime produced by these type of black holes. For the axially-symmetric case, we also make some general comments (independent of the underlying gravitational theory) on the relation between circular null geodesics and the fastest way to circle a black hole.Comment: In this post-publisher version two typos were corrected: the signature of the metric in eq.(1) and a factor in eq.(102). We thanks Gary Gibbons and Chris Pope for bringing to our attention these typo

A Jacobian elliptic single-field inflation

In the scenario of single-field inflation, this field is done in terms of Jacobian elliptic functions. This approach provides, when constrained to particular cases, analytic solutions already known in the past, generalizing them to a bigger family of analytical solutions. The emergent cosmology is analysed using the Hamilton-Jacobi approach and then, the main results are contrasted with the recent measurements obtained from the Planck 2015 data.Comment: 7 pages, 5 figure

Trade based on economies of scale under monopolistic competition: a clarification of Krugman's model

Although a major contribution to trade theory, Krugman’s 1979 demonstration that ‘trade can arise and lead to mutual gains even when countries are similar’ fails to make explicit the economic mechanisms that lead up to this result. The current paper attempts to fill this gap by addressing several questions that are implicit in Krugman’s demonstration but which he does not explicitly analyze: - What is the effect of trade upon the demand curve faced by the typical firm in each nation? - How do firms react to the change in the demand curves they face, and what is the short-term outcome of their behaviour? - Why do some firms fail? - What is the role of the failure of firms in the adjustment to the final free trade equilibrium?Krugman, intra-industry trade, economies of scale, monopolistic competition.

Green's functions from real-time bold-line Monte Carlo: spectral properties of the nonequilibrium Anderson impurity model

The nonequilibrium spectral properties of the Anderson impurity model with a chemical potential bias are investigated within a numerically exact real time quantum Monte Carlo formalism. The two-time correlation function is computed in a form suitable for nonequilibrium dynamical mean field calculations. Additionally, the evolution of the model's spectral properties are simulated in an alternative representation, defined by a hypothetical but experimentally realizable weakly coupled auxiliary lead. The voltage splitting of the Kondo peak is confirmed and the dynamics of its formation after a coupling or gate quench are studied. This representation is shown to contain additional information about the dot's population dynamics. Further, we show that the voltage-dependent differential conductance gives a reasonable qualitative estimate of the equilibrium spectral function, but significant qualitative differences are found including incorrect trends and spurious temperature dependent effects