arXiv subjects

E. M. F. Curado

Publications and source records attributed to E. M. F. Curado.

33 records · Page 2Linked to original sources

arXiv2004

The mutual co-implication of thermodynamics' first and second laws

In classical phenomenological thermodynamics the first and second laws can be regarded as independent statements. Statistical mechanics provides a microscopic substratum that explains thermodynamics in probabilistic terms via a microstate probability distribution ${p_i}$. We study here a hitherto unexplored microscopic connection between the two laws. Given an information measure (or entropic form), each of the two laws implies the other through the process $p_i \to p_i+dp_i$.

cond-mat.stat-mech↗

arXiv2004

Construction of coherent states for physical algebraic systems

We construct a general state which is an eigenvector of the annihilation operator of the Generalized Heisenberg Algebra. We show for several systems, which are characterized by different energy spectra, that this general state satisfies the minimal set of conditions required to obtain Klauder's minimal coherent states.

math-ph↗

arXiv2002

Non-linear generalization of the sl(2) algebra

We present a generalization of the sl(2) algebra where the algebraic relations are constructed with the help of a general function of one of the generators. When this function is linear this algebra is a deformed sl(2) algebra. In the non-linear case, the finite dimensional representations are constructed in two different ways. In the first case, which provides finite dimensional representations only for the non-linear case, these representations come from solutions to a dynamical equation and we show how to construct explicitly these representations for a general quadratic non-linear function. The other type of finite dimensional representation comes from solutions to a cut condition equation. We give examples of solutions of this type in the non-linear case as well.

math-ph↗

arXiv2002

Generalized quantum field theory: perturbative computation and perspectives

We analyze some consequences of two possible interpretations of the action of the ladder operators emerging from generalized Heisenberg algebras in the framework of the second quantized formalism. Within the first interpretation we construct a quantum field theory that creates at any space-time point particles described by a q-deformed Heisenberg algebra and we compute the propagator and a specific first order scattering process. Concerning the second one, we draw attention to the possibility of constructing this theory where each state of a generalized Heisenberg algebra is interpreted as a particle with different mass.

hep-th↗

arXiv2001

Heisenberg-type structures of one-dimensional quantum Hamiltonians

We construct a Heisenberg-like algebra for the one dimensional infinite square-well potential in quantum mechanics. The ladder operators are realized in terms of physical operators of the system as in the harmonic oscillator algebra. These physical operators are obtained with the help of variables used in a recently developed non commutative differential calculus. This \textquotedblleft square-well algebra\textquotedblright is an example of an algebra in a large class of generalized Heisenberg algebras recently constructed. This class of algebras also contains $q$-oscillators as a particular case. We also discuss the physical content of this large class of algebras.

hep-th↗

arXiv2001

Construction of a non-standard quantum field theory through a generalized Heisenberg algebra

We construct a Heisenberg-like algebra for the one dimensional quantum free Klein-Gordon equation defined on the interval of the real line of length $L$. Using the realization of the ladder operators of this type Heisenberg algebra in terms of physical operators we build a 3+1 dimensional free quantum field theory based on this algebra. We introduce fields written in terms of the ladder operators of this type Heisenberg algebra and a free quantum Hamiltonian in terms of these fields. The mass spectrum of the physical excitations of this quantum field theory are given by $\sqrt{n^2 π^2/L^2+m_q^2}$, where $n= 1,2,...$ denotes the level of the particle with mass $m_q$ in an infinite square-well potential of width $L$.

hep-th↗

arXiv2001

Multi Parametric Deformed Heisenberg Algebras: A Route to Complexity

We introduce a generalization of the Heisenberg algebra which is written in terms of a functional of one generator of the algebra, $f(J_0)$, that can be any analytical function. When $f$ is linear with slope $θ$, we show that the algebra in this case corresponds to $q$-oscillators for $q^2 = \tan θ$. The case where $f$ is a polynomial of order $n$ in $J_0$ corresponds to a $n$-parameter deformed Heisenberg algebra. The representations of the algebra, when $f$ is any analytical function, are shown to be obtained through the study of the stability of the fixed points of $f$ and their composed functions. The case when $f$ is a quadratic polynomial in $J_0$, the simplest non-linear scheme which is able to create chaotic behavior, is analyzed in detail and special regions in the parameter space give representations that cannot be continuously deformed to representations of Heisenberg algebra.

hep-th↗

arXiv2000

A nonextensive thermodynamical equilibrium approach in $e^+ e^- \to hadrons$

We show that the inclusion of long distance effect, expected in strong interactions, through a nonextensive thermodynamical approach is able to explain the experimental distribution of the transverse momentum of the hadrons with respect to the jet axis ($p_{t}$) $e^+ e^- \to hadron$ reaction. The observed deviation from the exponential behavior, predicted by the Boltzmann-Gibbs thermodynamical treatment, is automatically recovered by the nonextensive Tsallis statistics used here. We fitted the observed $p_{t}$ spectrum in the range of 14 GeV to 161 GeV and obtained, besides a good fit, the theoretical important fact that the temperature becomes independent of the primary energy.

hep-ph↗

arXiv2000

Thermodynamic Properties of a Solid Exhibiting the Energy Spectrum given by the Logistic Map

We show that the infinite-dimensional representation of the recently introduced Logistic algebra can be interpreted as a non-trivial generalization of the Heisenberg or oscillator algebra. This allow us to construct a quantum Hamiltonian having the energy spectrum given by the logistic map. We analyze the Hamiltonian of a solid whose collective modes of vibration are described by this generalized oscillator and compute the thermodynamic properties of the model in the two-cycle and r=3.6785 chaotic region of the logistic map.

cond-mat.stat-mech↗

arXiv1999

Universality in short-range Ising spin glasses

The role of the distribution of coupling constants on the critical exponents of the short-range Ising spin-glass model is investigated via real space renormalization group. A saddle-point spin glass critical point characterized by a fixed-point distribution is found in an appropriated parameter space. The critical exponents $β$ and $ν$ are directly estimated from the data of the local Edwards-Anderson order parameters for the model defined on a diamond hierarchical lattice of fractal dimension $d_{f}=3$. Four distinct initial distributions of coupling constants (Gaussian, bimodal, uniform and exponential) are considered; the results clearly indicate a universal behavior.

cond-mat.dis-nn↗

arXiv1998

Short Range Ising Spin Glasses: a critical exponent study

The critical properties of short-range Ising spin-glass models, defined on a diamond hierarchical lattice of graph fractal dimension $d_{f}=2.58$, 3, and 4, and scaling factor 2 are studied via a method based on the Migdal-Kadanoff renormalization-group scheme. The order parameter critical exponent $β$ is directly estimated from the data of the local Edwards- Anderson (EA) order parameter, obtained through an exact recursion procedure. The scaling of the EA order parameter, leading to estimates of the $ν$ exponent of the correlation length is also performed. Four distinct initial distributions of the quenched coupling constants (Gaussian, bimodal, uniform and exponential) are considered. Deviations from a universal behaviour are observed and analysed in the framework of the renormalized flow in a two dimensional appropriate parameter space.

cond-mat.dis-nn↗

arXiv1997

Short-Range Ising Spin Glass: Multifractal Properties

The multifractal properties of the Edwards-Anderson order parameter of the short-range Ising spin glass model on d=3 diamond hierarchical lattices is studied via an exact recursion procedure. The profiles of the local order parameter are calculated and analysed within a range of temperatures close to the critical point with four symmetric distributions of the coupling constants (Gaussian, Bimodal, Uniform and Exponential). Unlike the pure case, the multifractal analysis of these profiles reveals that a large spectrum of the $α$-Hölder exponent is required to describe the singularities of the measure defined by the normalized local order parameter, at and below the critical point. Minor changes in these spectra are observed for distinct initial distributions of coupling constants, suggesting an universal spectra behavior. For temperatures slightly above T_{c}, a dramatic change in the $F(α)$ function is found, signalizing the transition.

cond-mat.dis-nn↗

arXiv1996

Roundoff-induced Coalescence of Chaotic Trajectories

Numerical experiments recently discussed in the literature show that identical nonlinear chaotic systems linked by a common noise term (or signal) may synchronize after a finite time. We study the process of synchronization as function of precision of calculations. Two generic behaviors of the average coalescence time are identified: exponential or linear. In both cases no synchronization occurs if iterations are done with {\em infinite} precision.

chao-dyn↗

arXiv1995

Influence of Refractory Periods in the Hopfield model

We study both analytically and numerically the effects of including refractory periods in the Hopfield model for associative memory. These periods are introduced in the dynamics of the network as thresholds that depend on the state of the neuron at the previous time. Both the retrieval properties and the dynamical behaviour are analyzed.

cond-mat↗

arXiv1995

Distribution of Eigenvalues of Ensembles of Asymmetrically Diluted Hopfield Matrices

Using Grassmann variables and an analogy with two dimensional electrostatics, we obtain the average eigenvalue distribution $ρ(ω)$ of ensembles of $N \times N$ asymmetrically diluted Hopfield matrices in the limit $N \rightarrow \infty$. We found that in the limit of strong dilution the distribution is uniform in a circle in the complex plane.

cond-mat↗