Planck Scale Physics and Bogoliubov Spaces in a Bose-Einstein Condensate

We analyze the consequences caused by a deformed dispersion relation, suggested in several quantum gravity models, upon a bosonic gas. Concerning the ground state of the Bogoliubov space of this system, we deduce the corrections in the pressure, the speed of sound, and the corresponding healing length. Indeed, we prove that the corrections in the relevant thermodynamic properties associated with the ground state, defines a non trivial function of the density of particles and the deformation parameters, allowing us to constrain, in principle, the form of the modified energy-momentum dispersion relation

Black phosphorus: narrow gap, wide applications

The recent isolation of atomically thin black phosphorus by mechanical exfoliation of bulk layered crystals has triggered an unprecedented interest, even higher than that raised by the first works on graphene and other two-dimensional, in the nanoscience and nanotechnology community. In this Perspective we critically analyze the reasons behind the surge of experimental and theoretical works on this novel two-dimensional material. We believe that the fact that black phosphorus band gap value spans over a wide range of the electromagnetic spectrum that was not covered by any other two-dimensional material isolated to date (with remarkable industrial interest such as thermal imaging, thermoelectrics, fiber optics communication, photovoltaics, etc), its high carrier mobility, its ambipolar field-effect and its rather unusual in-plane anisotropy drew the attention of the scientific community towards this two-dimensional material. Here we also review the current advances, the future directions and the challenges in this young research field.Comment: Updated version of the perspective article about black phosphorus, including all the feedback received from arXiv users + reviewer

ARROW´S IMPOSSIBILITY THEOREM IS NOT SO IMPOSSIBLE AND CONDORCET´S PARADOX IS NOT SO PARADOXICAL: THE ADEQUATE DEFINITION OF A SOCIAL CHOICE PROBLEM

In this article, we do two things: first, we present an alternative and simplified proof of the known fact that cardinal individual utility functions are necessary, but not sufficient, and that interpersonal comparability is sufficient, but not necessary, for the construction of a social welfare function. This means that Arrow´s impossibility theorem is simply a consequence of forcing the individual utility functions to be ordinal. And second, based on this proof, this article establishes two necessary conditions for the adequate definition of a social choice problem. It is shown that, if these two conditions are satisfied, a number of desirable properties for a social choice are satisfied, including transitivity. This means that Condorcet´s paradox is simply the result of a social choice problem that is not well defined.Condition of independence of irrevelant alternatives, social choice, social welfare function, cardinality and interpersonal comparability, Arrow s impossibility theorem, Condorcet s paradox