Spontaneous Symmetry Breakdown in non-relativistic Quantum Mechanics

The advantages and disadvantages of some pedagogical non-relativistic quantum-mechanical models, used to illustrate spontaneous symmetry breakdown, are discussed. A simple quantum-mechanical toy model (a spinor on the line, subject to a magnetostatic interaction) is presented, that exhibits the spontaneous breakdown of an internal symmetry.Comment: 19 pages, 5 figures. arXiv admin note: substantial text overlap with arXiv:1111.1213. Equations (30) and (31) have been corrected. Other minor correction

Crystallization and melting of bacteria colonies and Brownian Bugs

Motivated by the existence of remarkably ordered cluster arrays of bacteria colonies growing in Petri dishes and related problems, we study the spontaneous emergence of clustering and patterns in a simple nonequilibrium system: the individual-based interacting Brownian bug model. We map this discrete model into a continuous Langevin equation which is the starting point for our extensive numerical analyses. For the two-dimensional case we report on the spontaneous generation of localized clusters of activity as well as a melting/freezing transition from a disordered or isotropic phase to an ordered one characterized by hexagonal patterns. We study in detail the analogies and differences with the well-established Kosterlitz-Thouless-Halperin-Nelson-Young theory of equilibrium melting, as well as with another competing theory. For that, we study translational and orientational correlations and perform a careful defect analysis. We find a non standard one-stage, defect-mediated, transition whose nature is only partially elucidated.Comment: 13 Figures. 14 pages. Submitted to Phys. Rev.

Tip charge dependence of three-dimensional AFM mapping of concentrated ionic solutions

A molecular scale understanding of the organization and structure of a liquid near a solid surface is currently a major challenge in surface science. It has implications across different fields from electrochemistry and energy storage to molecular biology. Three-dimensional AFM generates atomically resolved maps of solid-liquid interfaces. The imaging mechanism behind those maps is under debate, in particular, for concentrated ionic solutions. Theory predicts that the observed contrast should depend on the tip’s charged state. Here, by using neutrally, negatively, and positively charged tips, we demonstrate that the 3D maps depend on the tip’s polarization. A neutral tip will explore the total particle density distribution (water and ions) while a charged tip will reveal the charge density distribution. The experimental data reproduce the key findings of the theor

On the mass of the neutron star in Cyg X-2

We present new high resolution spectroscopy of the low mass X-ray binary Cyg X-2 which enables us to refine the orbital solution and rotational broadening of the donor star. In contrast with Elebert et al (2009) we find a good agreement with results reported in Casares et al. (1998). We measure $P=9.84450\pm0.00019$ day, $K_2=86.5\pm1.2$ km s$^{-1}$ and $V \sin i=33.7\pm0.9$ km s$^{-1}$. These values imply $q=M_{2}/M_{1}=0.34 \pm 0.02$ and $M_{1}=1.71\pm 0.21$ M$_{\odot}$ (for $i=62.5 \pm 4^{\circ}$). Therefore, the neutron star in Cyg X-2 can be more massive than canonical. We also find no evidence for irradiation effects in our radial velocity curve which could explain the discrepancy between Elebert et al's and our $K_2$ values.Comment: Accepted for publication in MNRA