arXiv subjects

L. Velazquez

Publications and source records attributed to L. Velazquez.

50 records · Page 3Linked to original sources

arXiv2003

Remarks about the microcanonical description of astrophysical systems

We reconsider some general aspects about the mean field thermodynamical description of the astrophysical systems based on the microcanonical ensemble. Starting from these basis, we devote a special attention to the analysis of the scaling laws of the thermodynamical variables and potentials in the thermodynamic limit. Geometrical considerations motivate a way by means of which could be carried out a well-defined generalized canonical-like description for this kind of systems, even being nonextensive. This interesting possibility allows us to extend the applicability of the Standard Thermodynamic methods, even in the cases in which the system exhibits a negative specific heat. As example of application, we reconsider the classical Antonov problem of the isothermal spheres.

cond-mat.stat-mech↗

arXiv2003

On the dynamical anomalies in the Hamiltonian Mean Field model

We study the N-dependence of the thermodynamical variables and the dynamical behavior of the well-known Hamiltonian Mean Field model. Microcanonical analysis revealed a thermodynamic limit which defers from the a priory traditional assumption of the N-dependence of the coupling constant g as 1/N: to tend N?infinity keeping constant E/N^3 and g/N, prescription which guarantees the extensivity of the Boltzmann entropy. The analysis of dynamics leads to approximate the time evolution of the magnetization density m by means of a Langevin equation with multiplicative noise. This equation leads to a Fokker-Planck's equation which is N-independent when the time variable is scaled by the N-dependent time constant T_{mac}=sqrt(IN/g), which represents the characteristic time scale for the dynamical evolution of the macroscopic observables derived from the magnetization density. This results explains the origin of the slow relaxation regimen observed in microcanonical numerical computations of dynamics of this model system. Connection with the system self-similarity is suggested.

cond-mat.stat-mech↗

arXiv2003

On the dynamical anomalies in numerical simulations of selfgravitating systems

According to self-similarity hypothesis, the thermodynamic limit could be defined from the scaling laws for the system self-similarity by using the microcanonical ensemble. This analysis for selfgravitating systems yields the following thermodynamic limit: send N to infinity, keeping constant E/N^{(7/3)} and LN^{(1/3)}, in which is ensured the extensivity of the Boltzmann entropy S_{B}=lnW(E,N). It is shown how the consideration of this thermodynamic limit allows us to explain the origin of dynamical anomalies in numerical simulations of selfgravitating systems.

cond-mat.stat-mech↗

arXiv2002

Astrophysical Systems: A model based on the Self-similarity Scaling Postulates

In the present work, it is developed a formalism to deal with the macroscopic study of the astrophysical systems, which is based on the consideration of the exponential self-similarity scaling laws that these systems exhibit during the realization of the thermodynamic limit. Due to their scaling laws, these systems are pseudoextensive, since although they are nonextensive in the usual sense, they can be studied by the Boltzmann-Gibbs Statistics if an appropriate representation of the integrals of motion of the macroscopic description is chosen. As example of application, it is analyzed the system of classical identical particles interacting via Newtonian interaction. A renormalization procedure is used in order to perform a well-defined macroscopic description of this system in quasi-stationary states, since it can not be in a real thermodynamic equilibrium. Our analysis showed that the astrophysical systems exhibit self-similarity under the following thermodynamic limit: $E\to \infty ,$ $L\to 0,$ $N\to \infty ,$ keeping $E/N^{7/3}=$const, $LN^{1/3}=$const, where $L$ is the characteristic linear dimension of the system. It is discussed the effect of these scaling laws in the dynamical properties of the system. In a general way, our solution exhibits the same features of the Antonov problem: the existence of the gravitational collapse at low energies as well as a region with a negative heat capacity.

cond-mat.stat-mech↗

arXiv2002

Differential properties of matrix orthogonal polynomials

In this paper a general theory of semi-classical matrix orthogonal polynomials is developed. We define the semi-classical linear functionals by means of a distributional equation $D(u A) = u B,$ where $A$ and $B$ are matrix polynomials. Several characterizations for these semi-classical functionals are given in terms of the corresponding (left) matrix orthogonal polynomials sequence. They involve a quasi-orthogonality property for their derivatives, a structure relation and a second order differo-differential equation. Finally we illustrate the preceding results with some non-trivial examples.

math.CA↗

arXiv2002

Microcanonical Aproach for the OLA Model

In the present paper it is analyzed a very simple example of pseudoextensive system, the tridimensional system of Linear Coupled Oscillators (OLA Model). The same one constitutes a classical tridimensional system of identical interacting particles by means of harmonic oscillators. This academic problem possesses a complete analytical solution allowing this way that it can find application in modeling some properties of the self-gravitating systems. It is shown that although this is a nonextensive system in the usual sense, it can be dealt in the thermodynamic limit with the usual Boltzmann-Gibbs' Statistics with an appropriate selection of the representation of the space of the integrals of motion.

cond-mat.stat-mech↗

arXiv2002

Remarks on Tsallis' Satistics

In the present paper the conditions for the validity of the Tsallis' Statistics are analyzed. The same has been done following the analogy with the traditional case: starting from the microcanonical description of the systems and taking into account their self-similarity scaling properties in the thermodynamic limit, it is analyzed the necessary conditions for the equivalence of microcanonical ensemble with the Tsallis' generalization of the canonical ensemble. It is shown that the Tsallis' Statistics is appropriate for the macroscopic description of systems with potential scaling laws of the asymptotic accessible states density of the microcanonical ensemble. Our analysis shows many details of the Tsallis' formalism: the q-expectation values, the generalized Legendre's transformations between the thermodynamic potentials, as well as the conditions for its validity, having a priori the possibility to estimate the value of the entropic index without the necessity of appealing to the computational simulations or the experiment. On the other hand, the definition of physical temperature received a modification which differs from the Toral's result. For the case of finite systems, we have generalized the microcanonical thermostatistics of D. H. E. Gross with the generalization of the curvature tensor for this kind of description.

cond-mat.stat-mech↗

arXiv2001

The microcanonical theory and pseudoextensive systems

In the present paper are considered the self-similarity scaling postulates in order to extend the Thermodynamics to the study of one special class of nonextensive systems: the pseudoextensive, those with exponential behavior for the asymptotical states density of the microcanonical ensemble. It is shown that this kind of systems could be described with the usual Boltzmann-Gibbs' Distribution with an appropriate selection of the representation of the movement integrals. It is shown that the pseudoextensive systems are the natural frame for the application of the microcanonical thermostatistics theory of D. H. E. Gross.

cond-mat.stat-mech↗

arXiv2001

Generalizing the Extensive Postulates

We addressed the problem of generalizing the extensive postulates of the standard thermodynamics in order to extend it to the study of nonextensive systems. We did it in analogy with the traditional analysis, starting from the microcanonical ensemble, but this time, considering its equivalence with some generalized canonical ensemble in the thermodynamic limit by means of the scaling properties of the fundamental physical observables.

cond-mat.stat-mech↗

arXiv2001

Microcanonical Thermostatistical Investigation of the Blackbody Radiation

In this work is presented the microcanonical analysis of the blackbody radiation. In our model the electromagnetic radiation is confined in an isolated container with volume V in which the radiation can not escape, conserving this way its total energy, E. Our goal is to precise the meaning of the Thermodynamic Limit for this system as well as the description of the nonextensive effects of the generalized Planck formula for the spectral density of energy. Our analysis shows the sterility of the intents of finding nonnextensive effects in normal conditions: the traditional description of the blackbody radiation is extraordinarily exact. The nonextensive effects only appear in the low temperature region, however, they are extremely difficult to detect.

cond-mat.stat-mech↗

arXiv2001

Where the Tsallis Statistic is valid?

In the present paper are analysed the conditions for the validity of the Tsallis Statistics. The same have been done following the analogy with the traditional case: starting from the microcanonical description of the systems and analysing the scaling properties of the fundamental macroscopic observables in the Thermodynamic Limit. It is shown that the Generalized Legendre Formalism in the Tsallis Statistic only could be applied for one special class of the bordering systems, those with non exponential growth of the accessible states density in the thermodynamic limit and zero-order divergency behavior for the fundamental macroscopic observables, systems located in the chaos threshold.

cond-mat↗

arXiv2001

Geometrical aspects in Equilibrium Thermodynamics

We discuss different aspects of the present status of the Statistical Physics focusing the attention on the non-extensive systems, and in particular, on the so called small systems. Multimicrocanonical Distribution and some of its geometric aspects are presented. The same could be a very atractive way to generalize the Thermodynamics. It is suggested that if the Multimicrocanonical Distribution could be equivalent in the Thermodynamic Limit with some generalized Canonical Distribution, then it is possible to estimate the entropic index of the non-extensive thermodynamics of Tsallis without any additional postulates.

cond-mat↗

arXiv2001

Some geometrical aspects of the Microcanonical Distribution

In the present work is presented some considerations for a possible generalization of the Microcanonical thermoestatics (M.Th) of D.H.E. Gross.The same reveals a geometric aspect that commonly it has been disregarded so far: the local reparametrization invariance . This new characteristic leads to the needing of generalizing the methods of M.Th to be consequent with this property.

cond-mat↗

arXiv1992

Electromagnetic Interaction of Anyons in Non-Relativistic Quantum Field Theory

The non-relativistic quantum field theoretic lagrangian which describes an anyon system in the presence of an electromagnetic field is identified. A non-minimal magnetic coupling to the Chern-Simons statistical field as well as to the electromagnetic field together with a direct coupling between between both fields are the non-trivial ingredients of the lagrangian obtained from the non-relativistic limit of the fermionic relativistic formulation. The results, an electromagnetic gyromagnetic ratio 2 for any spin together with a non-trivial dynamical spin dependent contact interaction between anyons as well as the spin dependence of the electromagnetic effective action, agree with the quantum mechanical formulation.

hep-th↗