Some Implications of the Cosmological Constant to Fundamental Physics

In the presence of a cosmological constant, ordinary Poincare' special relativity is no longer valid and must be replaced by a de Sitter special relativity, in which Minkowski space is replaced by a de Sitter spacetime. In consequence, the ordinary notions of energy and momentum change, and will satisfy a different kinematic relation. Such a theory is a different kind of a doubly special relativity. Since the only difference between the Poincare' and the de Sitter groups is the replacement of translations by certain linear combinations of translations and proper conformal transformations, the net result of this change is ultimately the breakdown of ordinary translational invariance. From the experimental point of view, therefore, a de Sitter special relativity might be probed by looking for possible violations of translational invariance. If we assume the existence of a connection between the energy scale of an experiment and the local value of the cosmological constant, there would be changes in the kinematics of massive particles which could hopefully be detected in high-energy experiments. Furthermore, due to the presence of a horizon, the usual causal structure of spacetime would be significantly modified at the Planck scale.Comment: 15 pages, lecture presented at the "XIIth Brazilian School of Cosmology and Gravitation", Mangaratiba, Rio de Janeiro, September 10-23, 200

Cosmological Term and Fundamental Physics

A nonvanishing cosmological term in Einstein's equations implies a nonvanishing spacetime curvature even in absence of any kind of matter. It would, in consequence, affect many of the underlying kinematic tenets of physical theory. The usual commutative spacetime translations of the Poincare' group would be replaced by the mixed conformal translations of the de Sitter group, leading to obvious alterations in elementary concepts such as time, energy and momentum. Although negligible at small scales, such modifications may come to have important consequences both in the large and for the inflationary picture of the early Universe. A qualitative discussion is presented which suggests deep changes in Hamiltonian, Quantum and Statistical Mechanics. In the primeval universe as described by the standard cosmological model, in particular, the equations of state of the matter sources could be quite different from those usually introduced.Comment: RevTeX, 4 pages. Selected for Honorable Mention in the Annual Essay Competition of the Gravity Research Foundation for the year 200

Living bacteria rheology: population growth, aggregation patterns and cooperative behaviour under different shear flows

The activity of growing living bacteria was investigated using real-time and in situ rheology -- in stationary and oscillatory shear. Two different strains of the human pathogen Staphylococcus aureus -- strain COL and its isogenic cell wall autolysis mutant -- were considered in this work. For low bacteria density, strain COL forms small clusters, while the mutant, presenting deficient cell separation, forms irregular larger aggregates. In the early stages of growth, when subjected to a stationary shear, the viscosity of both strains increases with the population of cells. As the bacteria reach the exponential phase of growth, the viscosity of the two strains follow different and rich behaviours, with no counterpart in the optical density or in the population's colony forming units measurements. While the viscosity of strain COL keeps increasing during the exponential phase and returns close to its initial value for the late phase of growth, where the population stabilizes, the viscosity of the mutant strain decreases steeply, still in the exponential phase, remains constant for some time and increases again, reaching a constant plateau at a maximum value for the late phase of growth. These complex viscoelastic behaviours, which were observed to be shear stress dependent, are a consequence of two coupled effects: the cell density continuous increase and its changing interacting properties. The viscous and elastic moduli of strain COL, obtained with oscillatory shear, exhibit power-law behaviours whose exponent are dependent on the bacteria growth stage. The viscous and elastic moduli of the mutant have complex behaviours, emerging from the different relaxation times that are associated with the large molecules of the medium and the self-organized structures of bacteria. These behaviours reflect nevertheless the bacteria growth stage.Comment: 9 pages, 10 figure

Nanometric pitch in modulated structures of twist-bend nematic liquid crystals

The extended Frank elastic energy density is used to investigate the existence of a stable periodically modulate structure that appears as a ground state exhibiting a twist-bend molecular arrangement. For an unbounded sample, we show that the twist-bend nematic phase $N_{TB}$ is characterized by a heliconical structure with a pitch in the nano-metric range, in agreement with experimental results. For a sample of finite thickness, we show that the wave vector of the stable periodic structure depends not only on the elastic parameters but also on the anchoring energy, easy axis direction, and the thickness of the sample.Comment: 11 page

Thermal entanglement witness for materials with variable local spin lengths

We show that the thermal entanglement in a spin system using only magnetic susceptibility measurements is restricted to the insulator materials. We develop a generalization of the thermal entanglement witness that allows us to get information about the system entanglement with variable local spin lengths that can be used experimentally in conductor or insulator materials. As an application, we study thermal entanglement for the half-filled Hubbard model for linear, square and cubic clusters. We note that it is the itinerancy of electrons that favors the entanglement. Our results suggest a weak dependence between entanglement and external spin freedom degrees.Comment: 4 pages, 3 figure

Radiative corrections in bumblebee electrodynamics

We investigate some quantum features of the bumblebee electrodynamics in flat spacetimes. The bumblebee field is a vector field that leads to a spontaneous Lorentz symmetry breaking. For a smooth quadratic potential, the massless excitation (Nambu-Goldstone boson) can be identified as the photon, transversal to the vacuum expectation value of the bumblebee field. Besides, there is a massive excitation associated with the longitudinal mode and whose presence leads to instability in the spectrum of the theory. By using the principal-value prescription, we show that no one-loop radiative corrections to the mass term is generated. Moreover, the bumblebee self-energy is not transverse, showing that the propagation of the longitudinal mode can not be excluded from the effective theory.Comment: Revised version: contains some more elaborated interpretation of the results. Conclusions improve