The twisted gradient flow coupling at one loop

We compute the one-loop running of the $SU(N)$ 't Hooft coupling in a finite volume gradient flow scheme using twisted boundary conditions. The coupling is defined in terms of the energy density of the gradient flow fields at a scale $\tilde{l}$ given by an adequate combination of the torus size and the rank of the gauge group, and is computed in the continuum using dimensional regularization. We present the strategy to regulate the divergences for a generic twist tensor, and determine the matching to the $\overline{\rm MS}$ scheme at one-loop order. For the particular case in which the twist tensor is non-trivial in a single plane, we evaluate the matching coefficient numerically and determine the ratio of $\Lambda$ parameters between the two schemes. We analyze the $N$ dependence of the results and the possible implications for non-commutative gauge theories and volume independence.Comment: 52 pages, 12 figure

The continuous star formation history of a giant HII region in M101

We present results about the star formation process in the giant HII region NGC 5471 in the outskirts of M101. From resolved HST/WPFC2 photometry we find that star formation has been going for the last 70 Myr. We further compare previous results from integrated infrared-optical photometry with the stellar resolved CMD and we discuss the star formation properties of this region and its individual knots, as well as characterizing the different stellar content. This result has very important consequences in our understanding of the burst versus continuous star formation activity in spiral galaxies.Comment: 2 pages, 2 figures. Proceeding of the conference From Stars to Galaxies: Building the pieces to build up the Universe (Venice, Italy

Matrix Product Density Operators: Renormalization Fixed Points and Boundary Theories

We consider the tensors generating matrix product states and density operators in a spin chain. For pure states, we revise the renormalization procedure introduced by F. Verstraete et al. in 2005 and characterize the tensors corresponding to the fixed points. We relate them to the states possessing zero correlation length, saturation of the area law, as well as to those which generate ground states of local and commuting Hamiltonians. For mixed states, we introduce the concept of renormalization fixed points and characterize the corresponding tensors. We also relate them to concepts like finite correlation length, saturation of the area law, as well as to those which generate Gibbs states of local and commuting Hamiltonians. One of the main result of this work is that the resulting fixed points can be associated to the boundary theories of two-dimensional topological states, through the bulk-boundary correspondence introduced by Cirac et al. in 2011.Comment: 63 pages, Annals of Physics (2016). Accepted versio

Matrix Product State Representations

This work gives a detailed investigation of matrix product state (MPS) representations for pure multipartite quantum states. We determine the freedom in representations with and without translation symmetry, derive respective canonical forms and provide efficient methods for obtaining them. Results on frustration free Hamiltonians and the generation of MPS are extended, and the use of the MPS-representation for classical simulations of quantum systems is discussed.Comment: Minor changes. To appear in QI

Unbounded violations of bipartite Bell Inequalities via Operator Space theory

In this work we show that bipartite quantum states with local Hilbert space dimension n can violate a Bell inequality by a factor of order $\sqrt{n}$ (up to a logarithmic factor) when observables with n possible outcomes are used. A central tool in the analysis is a close relation between this problem and operator space theory and, in particular, the very recent noncommutative $L_p$ embedding theory. As a consequence of this result, we obtain better Hilbert space dimension witnesses and quantum violations of Bell inequalities with better resistance to noise

Stable propagation of pulsed beams in Kerr focusing media with modulated dispersion

We propose the modulation of dispersion to prevent collapse of planar pulsed beams which propagate in Kerr-type self-focusing optical media. As a result, we find a new type of two-dimensional spatio-temporal solitons stabilized by dispersion management. We have studied the existence and properties of these solitary waves both analytically and numerically. We show that the adequate choice of the modulation parameters optimizes the stabilization of the pulse.Comment: 3 pages, 3 figures, submitted to Optics Letter

Parity effects in the scaling of block entanglement in gapless spin chains

We consider the Renyi alpha-entropies for Luttinger liquids (LL). For large block lengths l these are known to grow like ln l. We show that there are subleading terms that oscillate with frequency 2k_F (the Fermi wave number of the LL) and exhibit a universal power-law decay with l. The new critical exponent is equal to K/(2 alpha), where K is the LL parameter. We present numerical results for the anisotropic XXZ model and the full analytic solution for the free fermion (XX) point.Comment: 4 pages, 5 figures. Final version accepted in PR

Spatial genetic structure in the saddled sea bream (Oblada melanura [Linnaeus, 1758]) suggests multi-scaled patterns of connectivity between protected and unprotected areas in the Western Mediterranean Sea

Marine protected areas (MPAs) and networks of MPAs are advocated worldwide for the achievement of marine conservation objectives. Although the knowledge about population connectivity is considered fundamental for the optimal design of MPAs and networks, the amount of information available for the Mediterranean Sea is currently scarce. We investigated the genetic structure of the saddled sea bream ( Oblada melanura) and the level of genetic connectivity between protected and unprotected locations, using a set of 11 microsatellite loci. Spatial patterns of population differentiation were assessed locally (50-100 km) and regionally (500-1000 km), considering three MPAs of the Western Mediterranean Sea. All values of genetic differentiation between locations (Fst and Jost's D) were non-significant after Bonferroni correction, indicating that, at a relatively small spatial scale, protected locations were in general well connected with non-protected ones. On the other hand, at the regional scale, discriminant analysis of principal components revealed the presence of a subtle pattern of genetic heterogeneity that reflects the geography and the main oceanographic features (currents and barriers) of the study area. This genetic pattern could be a consequence of different processes acting at different spatial and temporal scales among which the presence of admixed populations, large population sizes and species dispersal capacity, could play a major role. These outcomes can have important implications for the conservation biology and fishery management of the saddled sea bream and provide useful information for genetic population studies of other coastal fishes in the Western Mediterranean Sea