Relativistic kinematics beyond Special Relativity

In the context of departures from Special Relativity written as a momentum power expansion in the inverse of an ultraviolet energy scale M, we derive the constraints that the relativity principle imposes between coefficients of a deformed composition law, dispersion relation, and transformation laws, at first order in the power expansion. In particular, we find that, at that order, the consistency of a modification of the energy-momentum composition law fixes the modification in the dispersion relation. We therefore obtain the most generic modification of Special Relativity that preserves the relativity principle at leading order in 1/M.Comment: Version with minor corrections, to appear in Phys. Rev.

Numerical solution of random differential models

This paper deals with the construction of a numerical solution of random initial value problems by means of a random improved Euler method. Conditions for the mean square convergence of the proposed method are established. Finally, an illustrative example is included in which the main statistics properties such as the mean and the variance of the stochastic approximation solution process are given. © 2011 Elsevier Ltd.This work has been partially supported by the Spanish M.C.Y.T. grants MTM2009-08587, DPI2010-20891-C02-01, Universidad Politecnica de Valencia grant PAID06-09-2588 and Mexican Conacyt.Cortés López, JC.; Jódar Sánchez, LA.; Villafuerte Altuzar, L.; Company Rossi, R. (2011). Numerical solution of random differential models. Mathematical and Computer Modelling. 54(7):1846-1851. https://doi.org/10.1016/j.mcm.2010.12.037S1846185154

Quantum critical behavior of electrons at the edge of charge order

We consider quantum critical points (QCP) in which quantum fluctuations associated with charge rather than magnetic order induce unconventional metallic properties. Based on finite-T calculations on a two-dimensional extended Hubbard model we show how the coherence scale T* characteristic of Fermi liquid behavior of the homogeneous metal vanishes at the onset of charge order. A strong effective mass enhancement reminiscent of heavy fermion behavior indicates the possible destruction of quasiparticles at the QCP. Experimental probes on quarter-filled layered organic materials are proposed for unveiling the behavior of electrons across the quantum critical region.Comment: 4 pages, 4 figures, accepted for publication in Phys. Rev. Let

Solving Riccati time-dependent models with random quadratic coefficient

This paper deals with the construction of approximate solutions of a random logistic differential equation whose nonlinear coefficient is assumed to be an analytic stochastic process and the initial condition is a random variable. Applying p-mean stochastic calculus, the nonlinear equation is transformed into a random linear equation whose coefficients keep analyticity. Next, an approximate solution of the nonlinear problem is constructed in terms of a random power series solution of the associate linear problem. Approximations of the average and variance of the solution are provided. The proposed technique is illustrated through an example where comparisons with respect to Monte Carlo simulations are shown. © 2011 Elsevier Ltd. All rights reserved.This work has been partially supported by the Spanish M.C.Y.T. grants MTM2009-08587, DPI2010-20891-C02-01, Universitat Politecnica de Valencia grant PAID06-09-2588 and Mexican Conacyt.Cortés López, JC.; Jódar Sánchez, LA.; Company Rossi, R.; Villafuerte Altuzar, L. (2011). Solving Riccati time-dependent models with random quadratic coefficient. Applied Mathematics Letters. 24(12):2193-2196. https://doi.org/10.1016/j.aml.2011.06.024S21932196241

Asymptotic approach to Special Relativity compatible with a relativistic principle

We propose a general framework to describe Planckian deviations from Special Relativity (SR) compatible with a relativistic principle. They are introduced as the leading corrections in an asymptotic approach to SR going beyond the energy power expansion of effective field theories. We discuss the conditions in which these Planckian effects might be experimentally observable in the near future, together with the non-trivial limits of applicability of this asymptotic approach that such a situation would produce, both at the very high (ultraviolet) and the very low (infrared) energy regimes.Comment: 12 page

Análisis de una propuesta de evaluación en relación con la estructura conceptual de la proporcionalidad

La presente propuesta es una aproximación reflexiva y critica de las prácticas evaluativas que se vienen desarrollando en la enseñanza básica y media en las instituciones de carácter privado de la ciudad de Cali, sustentada desde nuestra propia experiencia como docentes en ejercicio y estudiantes de último semestre en Licenciatura de Matemáticas y Física de la Universidad del Valle, y apoyada en el análisis de unas actividades piloto de intervención y evaluación matemática, en torno a diferentes nociones y conceptos relacionados con la estructura conceptual del tópico de proporción y proporcionalidad en los grados de séptimo de educación básica y décimo de educación media que se realizaron a fin de plantear una serie de interrogantes cruciales en torno a la evaluación, dado su carácter organizador, dinamizador y potencializador del currículo. Esta propuesta se apoyará en el marco metodológico de los organizadores del currículo, donde la evaluación es un eje fundamental en el análisis didáctico que permite la articulación y organización de un currículo significativo para los intereses de los educandos

Light-cone quantization of two dimensional field theory in the path integral approach

A quantization condition due to the boundary conditions and the compatification of the light cone space-time coordinate $x^-$ is identified at the level of the classical equations for the right-handed fermionic field in two dimensions. A detailed analysis of the implications of the implementation of this quantization condition at the quantum level is presented. In the case of the Thirring model one has selection rules on the excitations as a function of the coupling and in the case of the Schwinger model a double integer structure of the vacuum is derived in the light-cone frame. Two different quantized chiral Schwinger models are found, one of them without a $\theta$-vacuum structure. A generalization of the quantization condition to theories with several fermionic fields and to higher dimensions is presented.Comment: revtex, 14 p

Electron-phonon coupling in 122 Fe pnictides analyzed by femtosecond time-resolved photoemission

Based on results from femtosecond time-resolved photoemission, we compare three different methods for determination of the electron-phonon coupling constant {\lambda} in Eu and Ba-based 122 FeAs compounds. We find good agreement between all three methods, which reveal a small {\lambda} < 0.2. This makes simple electron-phonon mediated superconductivity unlikely in these compounds.Comment: 11 pages, 3 figure