Pseudogap, charge order, and pairing density wave at the hot spots in cuprate superconductors

We address the timely issue of the presence of charge ordering at the hot-spots in the pseudo-gap phase of cuprate superconductors in the context of an emergent SU(2)-symmetry which relates the charge and pairing sectors. Performing the Hubbard-Stratonovich decoupling such that the free energy stays always real and physically meaningful we exhibit three solutions of the spin-fermion model at the hot spots. A careful examination of their stability and free energy shows that, at low temperature, the system tends towards a co-existence of charge density wave (CDW) and the composite order parameter made of diagonal quadrupolar density wave and pairing fluctuations of Ref. [Nat. Phys. $\bf{9}$, 1745 (2013)].The CDW is sensitive to the shape of the Fermi surface in contrast to the diagonal quadrupolar order, which is immune to it. SU(2) symmetry within the pseudo-gap phase also applies to the CDW state, which therefore admits a pairing density pave counterpart breaking time reversal symmetry.Comment: 15 pages, 15 figures, final version + typo corrected in Eq. (12

Charge orders, magnetism and pairings in the cuprate superconductors

We review the recent developments in the field of cuprate superconductors with the special focus on the recently observed charge order in the underdoped compounds. We introduce new theoretical developments following the study of the antiferromagnetic (AF) quantum critical point (QCP) in two dimensions, in which preemptive orders in the charge and superconducting (SC) sectors emerged, that are in turn related by an SU(2) symmetry. We consider the implications of this proliferation of orders in the underdoped region, and provide a study of the type of fluctuations which characterize the SU(2) symmetry. We identify an intermediate energy scale where the SU(2) pairing fluctuations are dominant and argue that they are unstable towards the formation of a Resonant Peierls Excitonic (RPE) state at the pseudogap (PG) temperature $T^{*}$. We discuss the implications of this scenario for a few key experiments.Comment: 16 pages, 17 figure

The Two-Component Virial Theorem and the Physical Properties of Stellar Systems

Motivated by present indirect evidences that galaxies are surrounded by dark matter halos, we investigate whether their physical properties can be described by a formulation of the virial theorem which explicitly takes into account the gravitational potential term representing the interaction of the dark halo with the barionic or luminous component. Our analysis shows that the application of such a ``two-component virial theorem'' not only accounts for the scaling relations displayed, in particular, by elliptical galaxies, but also for the observed properties of all virialized stellar systems, ranging from globular clusters to galaxy clusters.Comment: 13 pages, 2 figures, LaTeX, corrected few typos. This version matches the published versio

Improved semiclassical density matrix: taming caustics

We present a simple method to deal with caustics in the semiclassical approximation to the thermal density matrix of a particle moving on the line. For simplicity, only its diagonal elements are considered. The only ingredient we require is the knowledge of the extrema of the Euclidean action. The procedure makes use of complex trajectories, and is applied to the quartic double-well potential.Comment: 20 pages, 7 figures. Revised version, accepted for publication in Phys. Rev.

Potencial produtivo do girassol consórciado com feijão no semiárido baiano.

O semiárido do nordeste baiano tem condições edafoclimáticas propícias ao desenvolvimento do girassol, à semelhança do que ocorre com o feijão. Assim foi objetivo deste trabalho conhecer o desempenho produtivo de cultivares de girassol nesta região, quando cultivadas em monocultivo e em consórcio com feijão, visando ampliar a área de adoção desta cultura. Os plantios experimentais foram realizados no município de Coronel João Sá, localizado no semiárido da Bahia no ano de 2010. Foram utilizadas os híbridos de girassol NTO 2.0, NTO 3.0, AGUARÁ 4, AGUARÁ 6, M 734, BRS 321, BRS 322, BRS 323, BRS G 26, OLISUN, PARAISO 22, PARAISO 33, PARAISO 65, HELIO 251, HELIO 253, HELIO 863 e as Variedades BRS 324, EMBRAPA122, MULTISSOL e CATISSOL. No consórcio utilizou-se a variedade de feijão carioca BRS Requinte. Foi estabelecido o rendimento de grãos de cada cultivar em cada um dos sistemas, monocultivo e consorciado. Na média, os rendimentos de grãos foram de 1.858 kg/ha, em monocultivo e 2.443 kg/ha, em consórcio com feijão. O sistema de plantio em consórcio com feijão foi mais favorável ao cultivo do girassol. A média geral de rendimento de grãos de girassol, na média dos sistemas de plantio adotados, foi de 2.151 kg/ha. As cultivares AGUARÁ 6, NTO 3.0, M 734, AGUARÁ 4, NTO 2.0, BRS 322, BRS 323, BRS G 26, OLISUN, HELIO 253 e HELIO 251, com rendimentos acima da média geral podem ser indicadas para o cultivo de girassol na região semiárida do Nordeste baiano, tanto para o monocultivo, como para o consórcio com o feijão. SUNFLOWER YIELD IN INTERCROPPING WITH BEAN IN THE SEMI-ARID OF BAHIA STATE. The semi-arid northeastern region of Bahia State has soil and climatic conditions for conducive to the development of the sunflower. Just aim of this study was to know the productive performance of sunflower cultivars in this region, when grown in monoculture and intercropping with bean. The experimental plantation were made in Coronel João Sá city, located in semi-arid region of Bahia in 2010. Were utilized the sunflower hybrids NTO 2.0, NTO 3.0, Aguará 4, Aguará 6, M 734, BRS 321, BRS 322, BRS 323, BRS G 26, OLISUN, PARAISO 22, PARAISO 33, PARAISO 65, HELIO 251, HELIO 253, HELIO 863 and the Varieties BRS 324, EMBRAPA122, MULTISSOL and CATISSOL. The bean variety BRS Requinte was used in the intercropping. It was established grain yield of each cultivar in each of the systems, monoculture and intercropping. On average, grain yields were 1,858 kg/ha in monoculture and 2,443 kg/ha in intercropping with bean. The planting system in intercropping with bean was more favorable to the sunflower cultivation. The average grain yield of sunflower in the mean of the cropping systems adopted, was 2,151 kg/ha. The Cultivars Aguará 6, NTO 3.0, M 734, Aguará 4, NTO 2.0, BRS 322, BRS 323, BRS G 26, OLISUN, HELIO 253 and HELIO 251, with yields above the general average can be indicated for the sunflower cultivation in the semi-arid northeastern region of Bahia in monoculture and in intercropping with bean