arXiv subjects

E. V. Correa Silva

Publications and source records attributed to E. V. Correa Silva.

13 recordsLinked to original sources

arXiv2010

Probing singularities in quantum cosmology with curvature scalars

We provide further evidence that the canonical quantization of cosmological models eliminates the classical Big Bang singularity, using the {\it DeBroglie-Bohm} interpretation of quantum mechanics. The usual criterion for absence of the Big Bang singularity in Friedmann-Robertson-Walker quantum cosmological models is the non-vanishing of the expectation value of the scale factor. We compute the `local expectation value' of the Ricci and Kretschmann scalars, for some quantum FRW models. We show that they are finite for all time. Since these scalars are elements of general scalar polynomials in the metric and the Riemann tensor, this result indicates that, for the quantum models treated here, the `local expectation value' of these general scalar polynomials should be finite everywhere. Therefore, we have further evidence that the quantization of the models treated here eliminates the classical Big Bang singularity. PACS: 04.40.Nr, 04.60.Ds, 98.80.Qc.

gr-qc↗

arXiv2007

Explorando Sistemas Hamiltonianos II: A Natureza de Pontos de Equilibrio Degenerados

Neste segundo artigo sobre sistemas Hamiltonianos, apresentamos o metodo da explosao para a determinacao da natureza de pontos fixos (pontos de equilibrio degenerados. Aplicamos o metodo a dois modelos hamiltonianos com um e dois graus de liberdade, respectivamente. Primeiramente, analisamos um sistema formado por um pendulo simples submetido a um torque externo constante T. Em seguida, consideramos um sistema formado por um pendulo duplo com segmentos de comprimentos e massas iguais, tambem submetidos a torques externos constantes e nao nulos. A presenca de pontos de equilibrio degenerados nos casos dos pendulos simples e duplo ocorre para certos valores dos torques externos. In this second article on Hamiltonian systems, we present the blow-up method for the determination of the nature of degenerate fixed points (equilibrium points). We apply the method to two hamiltonian models with one and two degrees of freedom, respectively. Firstly we study a system formed by a simple pendulum submitted to a constant external torque T. Then we consider a system formed by a double pendulum of segments with equal lengths and masses, also submitted to non-vanishing constant external torques. The presence of degenerate equilibrium points in both cases of simple and double pendulums occurs for some values of the external torques.

math-ph↗

arXiv2006

The high temperature expansion of the classical $XYZ$ chain

We present the $β$-expansion of the Helmholtz free energy of the classical $XYZ$ model, with a single-ion anisotropy term and in the presence of an external magnetic field, up to order $β^{12}$. We compare our results to the numerical solution of Joyce's [Phys. Rev. Lett. 19, 581 (1967)] expression for the thermodynamics of the $XXZ$ classical model, with neither single-ion anisotropy term nor external magnetic field. This comparison shows that the derived analytical expansion is valid for intermediate temperatures such as $kT/J_x \approx 0.5$. We show that the specific heat and magnetic susceptibility of the spin-2 antiferromagnetic chain can be approximated by their respective classical results, up to $kT/J \approx 0.8$, within an error of 2.5%. In the absence of an external magnetic field, the ferromagnetic and antiferromagnetic chains have the same classical Helmholtz free energy. We show how this two types of media react to the presence of an external magnetic field.

cond-mat.stat-mech↗

arXiv2005

Quantization of Friedmann-Robertson-Walker spacetimes in the presence of a negative cosmological constant and radiation

We quantize three Friedmann-Robertson-Walker models in the presence of a negative cosmological constant and radiation. The models differ from each other by the constant curvature of the spatial sections, which may be positive, negative or zero. They give rise to Wheeler-DeWitt equations for the scale factor which have the form of the Schroedinger equation for the quartic anharmonic oscillator. We find their eigenvalues and eigenfunctions by using a method first developed by Chhajlany and Malnev, and use the eigenfunctions in order to construct wave packets for each case and evaluate the time-dependent expected value of the scale factors. We find for all of them that the expected values of the scale factors oscillate between maximum and minimum values. Since the expectation values of the scale factors never vanish, we conclude that these models do not have singularities.

gr-qc↗

arXiv2005

Thermodynamics of the quantum spin-S XXZ chain

The thermodynamics of the spin-$S$ anisotropic quantum $XXZ$ chain with arbitrary value of $S$ and unitary norm, in the high-temperature regime, is reported. The single-ion anisotropy term and the interaction with an external magnetic field in the $z$-direction are taken into account. We obtain, for arbitrary value of $S$, the $β$-expansion of the Helmholtz free energy of the model up to order $β^6$ and show that it actually depends on $\frac{1}{S(S+1)}$. Its classical limit is obtained by simply taking $S\to \infty$. At $h=0$ and D=0, our high temperature expansion of the classical model coincides with Joyce's exact solution\cite{joyce_prl}. We study, in the high temperature region, some thermodynamic quantities such as the specific heat and the magnetic susceptibility as functions of spin and verify for which values of $S$ those thermodynamic functions behave classically. Their finite temperature behavior is inferred from interpolation of their high- and low-temperature behavior, and shown to be in good agreement with numerical results. The finite temperature behavior is shown for higher values of spin.

cond-mat.str-el↗

arXiv2005

Thermodynamics of the S=1 spin ladder as a composite S=2 chain model

A special class of S=1 spin ladder hamiltonians, with second- neighbor exchange interactions and with anisotropies in the $z$-direction, can be mapped onto one-dimensional composite S=2 (tetrahedral S=1) models. We calculate the high temperature expansion of the Helmoltz free energy for the latter class of models, and show that their magnetization behaves closely to that of standard XXZ models with a suitable effective spin $S_{eff}$, such that $S_{eff}(1+S_{eff})=< \vec{\bf S}_i^2>$, where ${\bf S}_i$ refers to the components of spin in the composite model. It is also shown that the specific heat per site of the composite model, on the other hand, can be very different from that of the effective spin model, depending on the parameters of the hamiltonian.

cond-mat.str-el↗

arXiv2002

Qualitative Study of a Robot Arm as a Hamiltonian System

A double pendulum subject to external torques is used as a model to study the stability of a planar manipulator with two links and two rotational driven joints. The hamiltonian equations of motion and the fixed points (stationary solutions) in phase space are determined. Under suitable conditions, the presence of constant torques does not change the number of fixed points, and preserves the topology of orbits in their linear neighborhoods; two equivalent invariant manifolds are observed, each corresponding to a saddle-center fixed point.

cs.RO↗

arXiv2002

A Comment on the beta-expansion of s=1/2 and s=1 Ising Models

The purpose of the present work is to apply the method recently developed in reference [chain_m] to the spin-1 Ising chain, showing how to obtain analytical $β$-expansions of thermodynamical functions through this formalism. In this method, we do not solve any transfer matrix-like equations. A comparison between the $β$-expansions of the specific heat and the magnetic susceptibility for the $s=1/2$ and $s=1$ one-dimensional Ising models is presented. We show that those expansions have poorer convergence when the auxiliary function of the model has singularities.

cond-mat↗

arXiv2000

Analytical Results of the One-Dimensional Hubbard Model in the High Temperature Limit

We investigate the grand potential of the one-dimensional Hubbard model in the high temperature limit, calculating the coefficients of the high temperature expansion ($β$-expansion) of this function up to order $β^4$ by an alternative method. The results derived are analytical and do not involve any perturbation expansion in the hopping constant, being valid for arbitrary density of electrons in the one-dimensional model. In the half-filled case, we compare our analytical results for the specific heat and the magnetic susceptibility, in the high-temperature limit, with the ones obtained by Beni {\it et al.} and Takahashi's integral equations, showing that the latter result does not take into account the complete energy spectrum of the one-dimensional Hubbard model. The exact integral solution by Jüttner {\it et al}. is applied to the determination of the range of validity of our expansion in $β$ in the half-filled case, for several different values of $U$.

cond-mat↗

arXiv1999

Numerical Calculations Using Maple: Why & How?

The possibility of interaction between Maple and numeric compiled languages in performing extensive numeric calculations is exemplified by the Ndynamics package, a tool for studying the (chaotic) behavior of dynamical systems. Programming hints concerning the construction of Ndynamics are presented. The system command, together with the application of the black-box concept, is used to implement a powerful cooperation between Maple code and some other numeric language code.

math.NA↗

arXiv1998

On the Electromagnetic Response of Charged Bosons Coupled to a Chern-Simons Gauge Field: A Path Integral Approach

We analyze the electromagnetic response of a system of charged bosons coupled to a Chern-Simons gauge field. Path integral techniques are used to obtain an effective action for the particle density of the system dressed with quantum fluctuations of the CS gauge field. From the action thus obtained we compute the U(1) current of the theory for an arbitrary electromagnetic external field. For the particular case of a homogeneous external magnetic field, we show that the quantization of the transverse conductivity is exact, even in the presence of an arbitrary impurity distribution. The relevance of edge states in this context is analyzed. The propagator of density fluctuations is computed, and an effective action for the matter density in the presence of a vortex excitation is suggested.

cond-mat.mes-hall↗

arXiv1997

Analytical Results for the Grand-Canonical Partition Function for Unidimensional Hubbard Model up to Order $β^5$

We calculate the exact analytical coefficients of the $β$ expansion of the grand-canonical partition function of the unidimensional Hubbard model up to order $β^5$, using an alternative method, based on properties of the Grassmann algebra. The results derived are non-perturbative and no restrictions on the set of parameters that characterize the model are required. By applying this method we obtain analytical results for the thermodynamical quantities, in the high-temeprature limit, for arbitrary density of electrons in the unidimensional chain.

cond-mat.str-el↗

arXiv1996

Grand Canonical Partition Function for Unidimensional Systems: Application to Hubbard Model up to Order beta^3

We exploit the grassmannian nature of the variables involved in the path integral expression of the grand canonical partition function for self--interacting fermionic models to show, in one-space dimension, a general relation among the terms of it expansion in the high temperature limit and a combination of co-factors of a suitable matrix with commuting entries. As an application, we apply this framework to calculate the exact coefficients, up to order β^3, of the expansion of the grand canonical partition function for the Hubbard model in d=(1+1) in the high temperature limit. The results are valid for any set of parameters that characterize the model.

cond-mat↗