Strictly isospectral Bianchi type II cosmological models
We show that, in the Q=0 factor ordering, the Wheeler-DeWitt equation for the Bianchi type ll mod... more We show that, in the Q=0 factor ordering, the Wheeler-DeWitt equation for the Bianchi type ll model with the Ansatz \rm \Psi=A\, e^{\pm \Phi(q^{\mu})}, due to its one-dimensional character, may be approached by the strictly isospectral Darboux-Witten technique in standard supersymmetric quantum mechanics. One-parameter families of cosmological potentials and normalizable `wavefunctions of the universe' are exhibited. The isospectral method can be used to introduce normalizable wavefunctions in quantum cosmology
We present a very simple electronic implementation of the tent map, one of the best-known discret... more We present a very simple electronic implementation of the tent map, one of the best-known discrete dynamical systems. This is achieved by using integrated circuits and passive elements only. The experimental behavior of the tent map electronic circuit is compared with its numerical simulation counterpart. We find that the electronic circuit presents fixed points, periodicity, period doubling, chaos and intermittency that match with high accuracy the corresponding theoretical values.
We describe an algorithm for the continuous monitoring of the biomass and ethanol concentrations ... more We describe an algorithm for the continuous monitoring of the biomass and ethanol concentrations as well as the growth rate in the Mezcal fermentation process. The algorithm performs its task having available only the on-line measurements of the redox potential. The procedure combines an artificial neural network (ANN) that relates the redox potential to the ethanol and biomass concentrations with a nonlinearobserver-based algorithm that uses the ANN biomass estimations to infer the growth rate of this fermentation process. The results show that the redox potential is a valuable indicator of the metabolic activity of the microorganisms during the Mezcal fermentation. In addition, the estimated growth rate can be considered as a direct evidence of the presence of mixed culture growth in the process. Usually, mixtures of microorganisms could be intuitively clear in this kind of processes, however the total biomass data do not provide definite evidence by themselves. In this paper, the detailed design of the software sensor is presented, as well as its experimental application at the laboratory level.
A wavelet scaling numerical characterization of time series based on the variance of the wavelet ... more A wavelet scaling numerical characterization of time series based on the variance of the wavelet coefficients is used for three well-known four-dimensional and one five-dimensional hyper-chaotic systems. We report several scaling behaviors for the states of these hyper-chaotic systems.
Fisher’s arrow of time is introduced in quantum cosmology. Assuming that the evolution of the uni... more Fisher’s arrow of time is introduced in quantum cosmology. Assuming that the evolution of the universe in phase space starts from an initial squeezed cosmological state towards a final thermal one, a Fokker-Planck equation for the time-dependent, cosmological Q phase space probability distribution can be written down. Next, using some recent results in the literature, we derive an information arrow of time for the Fisher phase space cosmological entropy. We also mention the application of Fisher’s arrow of time to stochastic inflation models. Essay written for Gravity Research Foundation, 1997 [gr-qc/9703051] 1.- Quantum gravity and quantum cosmology cannot escape phase space approaches [1], which have proven so useful in both pure and applied physics ever since the first phase space formulations of quantum mechanics have been given by Wigner in 1932 and Husimi in 1940. In the area of quantum optics there has been substantial progress precisely as an outcome of the c-number phase sp...
Application of the double Darboux method to the quantum Taub continuum Abstract The strictly isos... more Application of the double Darboux method to the quantum Taub continuum Abstract The strictly isospectral double Darboux method is applied to the quantum Taub model in order to generate a one-parameter family of strictly isospectral potentials for this case. The family we build is based on a scattering Wheeler-DeWitt solution first discussed by Ryan and collaborators that we slightly modified according to a suggestion due to Dunster. The isospectral Taub potentials possess different (attenuated) scattering states with respect to the original Taub potential. Quantum cosmology and its supersymmetric extension [1] are an interesting " laboratory " for techniques of current use in nonrelativistic quantum mechanics. One such technique is the strictly isospectral double Darboux method, which is intimately connected to Witten's supersymmetric quantum mechanics [2]. We have already applied the double Darboux method to closed, radiation-filled Friedmann-Robertson-Walker (FRW) qu...
Q Deformation of the Singular Oscillator by Intertwining
We present a version of q-deformed calculus for the x^{-2} singular oscillator based on deformed ... more We present a version of q-deformed calculus for the x^{-2} singular oscillator based on deformed counterparts of Darboux intertwining operators. The case in which the deformed transformation function is of the vacuum type is detailed. It leads to second-order deformed operators which may be considered as supersymmetric partners, though for a sort of open systems, i.e., those possessing q-nonlocal "friction" terms, potential part, as well as vacuum fluctuations. The undeformed limit corresponds to the conservative case, since all q-nonlocalities wash ou
A previous work on the Ermakov approach for empty FRW minisuperspace universes of Hartle-Hawking ... more A previous work on the Ermakov approach for empty FRW minisuperspace universes of Hartle-Hawking factor ordering parameter Q=0 is extended to the Q not zero cases
Electromagnetic wave propagation in alternating material-metamaterial layered structures
arXiv: Optics, 2016
Using the transfer matrix method, we examine the parametric behavior of the transmittance of an e... more Using the transfer matrix method, we examine the parametric behavior of the transmittance of an electromagnetic plane wave propagating in the lossless regime through a periodic multilayered system as a function of the frequency and angle of incidence of the electromagnetic wave for the case in which the periodic structure comprises alternating material-metamaterial layers. A specific example of high transmittance at any angle of incidence in the visible region of the spectrum is identified
This is the English version of a friendly graduate course on Classical Mechanics, containing abou... more This is the English version of a friendly graduate course on Classical Mechanics, containing about 80% of the material I covered during the January-June 1999 semester at IFUG in the Mexican city of Leon. For the Spanish version, see physics/9906066
arXiv: General Relativity and Quantum Cosmology, 2007
The dynamical systems observability properties of barotropic bosonic and fermionic FRW cosmologic... more The dynamical systems observability properties of barotropic bosonic and fermionic FRW cosmological oscillators are investigated. Nonlinear techniques for dynamical analysis have been recently developed in many engineering areas but their application has not been extended beyond their standard field. This paper is a small contribution to an extension of this type of dynamical systems analysis to FRW barotropic cosmologies. We find that determining the Hubble parameter of barotropic FRW universes does not allow the observability, i.e., the determination of neither the barotropic FRW zero mode nor of its derivative as dynamical cosmological states. Only knowing the latter ones correspond to a rigorous dynamical observability in barotropic cosmology
Factorizations of ODEs with polynomial nonlinearities
We propose a factorization scheme for ordinary differential equations with polynomial nonlinearit... more We propose a factorization scheme for ordinary differential equations with polynomial nonlinearities (reaction-diffusion in the traveling frame and dampedanharmonic-oscillator equations) which is different and more efficient than that given by L.M. Berkovich in Sov. Math. Dokl. 45, 162 (1992). We then invert the factorization brackets in the SUSYQM style to get ODE’s with a different polynomial nonlinearity but displaying kink solutions of different width propagating at the same velocity as the kink solution of the original equation. We thus report an interesting pairing of this class of differential equations from the standpoint of their kink solutions that could have applications still unforeseen. We illustrate the mathematical procedure with several important cases, among which the generalized Fisher equation and the FitzHugh-Nagumo equation.
We obtain a class of parametric oscillation modes that we call K-modes with damping and absorptio... more We obtain a class of parametric oscillation modes that we call K-modes with damping and absorption that are connected to the classical harmonic oscillator modes through the "supersymmetric" one-dimensional matrix procedure similar to relationships of the same type between Dirac and Schrödinger equations in particle physics. When a single coupling parameter, denoted by K, is used, it characterizes both the damping and the dissipative features of these modes. Generalizations to several K parameters are also possible and lead to analytical results. If the problem is passed to the physical optics (and/or acoustics) context by switching from the oscillator equation to the corresponding Helmholtz equation, one may hope to detect the K-modes as waveguide modes of specially designed waveguides and/or cavities.
A one-parameter family of time dependent adiabatic indices is introduced for any given type of co... more A one-parameter family of time dependent adiabatic indices is introduced for any given type of cosmological fluid of constant adiabatic index by a mathematical method belonging to the class of Darboux transformations. The procedure works for zero cosmological constant at the price of introducing a new constant parameter related to the time dependence of the adiabatic index. I argue that these are the real cosmological fluids that are encountered at cosmological scales and that they can provide a simple and efficient explanation for the recent experimental findings regarding the present day accelerating universe. Draft of submission date: March 28, Yr 2·10 a.C. 1 Recent data from type Ia supernovae that can still be considered as meager provoked tremendous interest since they indicate that the universe has now an accelerating large scale expansion [1] (ρ + 3p < 0 in eq. 1 Institute of Physics, Guanajuato State University, P.O. Box E-143, Leon, Gto, Mexico. International Center for...
Guided by the analogy with the Rayleigh-Plesset dynamics of multielectron bubbles in superfluid H... more Guided by the analogy with the Rayleigh-Plesset dynamics of multielectron bubbles in superfluid He-4, we consider the cosmological FLRW evolution equation with additional cubic and sixth powers of the inverse of the scale factor of the universe. For the barotropic parameter w = 2/3 (coasting universe), along with zero cosmological constant in the absence of viscous terms, by using the Sundman time as evolution parameter, we present parametric solutions for the scale factor of the universe in terms of rational expressions of Weierstrass elliptic functions and their particular cases thereof. For other values of the equation of state parameter w, such as w = -1, but also the same coasting case, we present a more standard discussion in the conformal time variable using solutions obtained by numerical integration.
Después de una breve revisión de la historia de los alótropos del carbono conocidos al momento,no... more Después de una breve revisión de la historia de los alótropos del carbono conocidos al momento,nos enfocamos en el más reciente de ellos, el grafeno, cuyas propiedades extraordinariasse deben a la propagación relativista de sus electrones de conducción. Estas mismaspropiedades dan esperanzas para muchas aplicaciones tecnológicas de gran impacto.
We use a simple method that leads to the integrals involved in obtaining the travelling-wave solu... more We use a simple method that leads to the integrals involved in obtaining the travelling-wave solutions of wave equations with one and two exponential nonlinearities. When the constant term in the integrand is zero, implicit solutions in terms of hypergeometric functions are obtained, while when that term is nonzero, all the basic travelling-wave solutions of Liouville, Tzitzéica, and their variants, as as well sine/sinh-Gordon equations with important applications in the phenomenology of nonlinear physics and dynamical systems are found through a detailed study of the corresponding elliptic equations.
We show that a simple modification of the Lagrangian proposed by Padmanabhan in the paper [Mod. P... more We show that a simple modification of the Lagrangian proposed by Padmanabhan in the paper [Mod. Phys. Lett. A 33, 1830005 (2018)] leads to the most general dynamical invariant in [Ray and Reid, Phys. Lett. A 71, 317 (1979)].
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Papers by Haret Rosu