Fermion masses in a model for spontaneous parity breaking

In this paper we discuss a left-right symmetric model for elementary particles and their connection with the mass spectrum of elementary fermions. The model is based on the group $SU(2)_L\otimes SU(2)_R\otimes U(1)$. New mirror fermions and a minimal set of Higgs particles that breaks the symmetry down to $U(1)_{em}$ are proposed. The model can accommodate a consistent pattern for charged and neutral fermion masses as well as neutrino oscillations. An important consequence of the model is that the connection between the left and right sectors can be done by the neutral vector gauge bosons Z and a new heavy Z'.Comment: 7 pages, 3 figures. Accepted in Eur. Phys. J.

Dynamical complexity of discrete time regulatory networks

Genetic regulatory networks are usually modeled by systems of coupled differential equations and by finite state models, better known as logical networks, are also used. In this paper we consider a class of models of regulatory networks which present both discrete and continuous aspects. Our models consist of a network of units, whose states are quantified by a continuous real variable. The state of each unit in the network evolves according to a contractive transformation chosen from a finite collection of possible transformations, according to a rule which depends on the state of the neighboring units. As a first approximation to the complete description of the dynamics of this networks we focus on a global characteristic, the dynamical complexity, related to the proliferation of distinguishable temporal behaviors. In this work we give explicit conditions under which explicit relations between the topological structure of the regulatory network, and the growth rate of the dynamical complexity can be established. We illustrate our results by means of some biologically motivated examples.Comment: 28 pages, 4 figure

Topological Approach to Microcanonical Thermodynamics and Phase Transition of Interacting Classical Spins

We propose a topological approach suitable to establish a connection between thermodynamics and topology in the microcanonical ensemble. Indeed, we report on results that point to the possibility of describing {\it interacting classical spin systems} in the thermodynamic limit, including the occurrence of a phase transition, using topology arguments only. Our approach relies on Morse theory, through the determination of the critical points of the potential energy, which is the proper Morse function. Our main finding is to show that, in the context of the studied classical models, the Euler characteristic $\chi(E)$ embeds the necessary features for a correct description of several magnetic thermodynamic quantities of the systems, such as the magnetization, correlation function, susceptibility, and critical temperature. Despite the classical nature of the studied models, such quantities are those that do not violate the laws of thermodynamics [with the proviso that Van der Waals loop states are mean field (MF) artifacts]. We also discuss the subtle connection between our approach using the Euler entropy, defined by the logarithm of the modulus of $\chi(E)$ per site, and that using the {\it Boltzmann} microcanonical entropy. Moreover, the results suggest that the loss of regularity in the Morse function is associated with the occurrence of unstable and metastable thermodynamic solutions in the MF case. The reliability of our approach is tested in two exactly soluble systems: the infinite-range and the short-range $XY$ models in the presence of a magnetic field. In particular, we confirm that the topological hypothesis holds for both the infinite-range ($T_c \neq 0$) and the short-range ($T_c = 0$) $XY$ models. Further studies are very desirable in order to clarify the extension of the validity of our proposal

An efficient prescription to find the eigenfunctions of point interactions Hamiltonians

A prescription invented a long time ago by Case and Danilov is used to get the wave function of point interactions in two and three dimensions.Comment: 6 page

Magnetism and Electronic Correlations in Quasi-One-Dimensional Compounds

In this contribution on the celebration of the 80th birthday anniversary of Prof. Ricardo Ferreira, we present a brief survey on the magnetism of quasi-one-dimensional compounds. This has been a research area of intense activity particularly since the first experimental announcements of magnetism in organic and organometallic polymers in the mid 80s. We review experimental and theoretical achievements on the field, featuring chain systems of correlated electrons in a special AB2 unit cell structure present in inorganic and organic compounds