R. F. Alvarez-Estrada

Escort mean values and the characterization of power-law-decaying probability densities

Escort mean values (or q-moments) constitute useful theoretical tools for describing basic features of some probability densities such as those which asymptotically decay like power laws. They naturally appear in the study of many complex dynamical systems, particularly those obeying nonextensive statistical mechanics, a current generalization of the Boltzmann–Gibbs theory. They recover standard mean values (or moments) for q=1. Here we discuss the characterization of a (non-negative) probability density by a suitable set of all its escort mean values together with the set of all associated normalizing quantities, provided that all of them converge. This opens the door to a natural extension of the well-known characterization, for the q=1 instance, of a distribution in terms of the standard moments, provided that all of them have finite values. This question would be specially relevant in connection with probability densities having divergent values for all nonvanishing standard moments higher than a give...

Scattering of TM Waves by Dielectric Fibres Iterative and Eikonal Solutions

The scattering of electromagnetic waves by dielectric cylinders and, in particular, by optical fibres is studied through integral equations. The convergence of the iterations of the integral equations is established under certain conditions. The latter are satisfied for long wavelengths, and for optical fibres and wavelengths, when the dielectric permeability variation is rather small. An approximate eikonal solution is applied to optical fibres, and its reliability is discussed. A systematic procedure for estimating corrections to the eikonal approximation is proposed.

Renormalization constants for the propagator of the stochastically quantized Yang-Mills field theory

Abstract Within the method of stochastic quantization, the calculation of the three renormalization constants of the gauge field propagator for the continuum euclidean non-abelian Yang-Mills field theory is carried out. We introduce the gauge fixing term of Zwanziger and some similarities between the usual Faddeev-Popov and the equilibrium theory we obtain are discussed.

ß-function for Yang-Mills field theory in stochastic quantization

Abstract The universal s-function and a renormalization constant for the vertex corresponding to Yang-Mills theory within the stochastic quantization approach are calculated. The renormalization is done in the MS scheme. The same result is found for the s-function as in the usual Faddeev-Popov theory to the first relevant order in g ( g 3 ).

Schwinger and Thirring models at finite chemical potential and temperature

The imaginary time generating functional Z for the assless Schwinger model at nonzero chemical potential mu and temperature T is studied in a torus with spatial length L. The lack of Hermiticity of the Dirac operator gives rise to a nontrivial μ- and T-dependent phase J in the effective action. When the Dirac operator has no zero modes (trivial sector), we evaluate J, which is a topological contribution, and we find exactly Z, the thermodynamical partition function, the boson propagator and the thermally averaged Polyakov loop. The μ-dependent contribution of the free partition function cancels exactly the nonperturbative one from J, for L→∞, yielding a zero charge density for the system, which bosonizes at nonzero μ. The boson mass is e/√π, independent of T and μ, which is also the inverse correlation length between two opposite charges. Both the boson propagator and the Polyakov loop acquire a new T- and μ -dependent term at L→∞,. The imaginary time generating functional for the massless Thirring model at nonzero T and μ is obtained exactly in terms of the above solution of the Schwinger model in the trivial sector. For this model, the μ dependences of the thermodynamical partition function, the total fermion number density and the fermion two- point correlation function are obtained. The phase J displayed here leads to our new results and allows us to complement nontrivially previous studies on those models.

The time duration for DNA thermal denaturation

Motivated by the thermal denaturation of DNA, we consider two interacting three-dimensional macromolecular chains, bound to each other, in a medium at thermal equilibrium from about room temperature up to about the melting one (Tm), at which they become unbound. We outline models for the non-equilibrium evolution of the double-stranded system, based upon the Smoluchowski equation, and allow for heterogeneities, excluded-volume effects and hydrodynamic interactions. A moment method leads us to approximate the Smoluchowski equation by a one-dimensional differential equation for the lowest order moment, containing a global effective potential between the two strands. We concentrate on the time duration (τ) required for thermal denaturation to occur, for long times and temperature . Here τ is approximated by the so-called mean first passage time (MFPT) for the relative separation of the centres of mass of the two chains. An approximate formula for the MFPT is obtained and employed for estimates. The consistency of the MFPT with experimental results is discussed for both Rouse and Zimm regimes.

Field-theoretic study of the nonlinear Fokker-Planck equation

A new field-theoretic formulation of the Fokker-Planck approach to non-equilibrium statistical mechanics is presented. Starting with the nonlinear functional Fokker-Planck equation, a new generating functional is derived. No use of auxiliary conjugate fields or response functions is needed. The Feynman rules are deduced, and the renormalisation of the theory is carried out. Finally, the renormalisation group equation is solved, and scaling laws and critical exponents are calculated, which are in good agreement with previous results obtained through different formalisms.

Effective chiral lagrangian from QCD at nonzero chemical potential

We start from the euclidean QCD action for gluons and massless quarks with N_c colours at finite baryon chemical potential μ_B and zero temperature. For μ_B of the order of external momenta o(p) we derive an euclidean effective real chiral lagrangian at finite μ_B, up to and including o(pˆ4), in terms of Goldstone Bosons (GB), in the large N_c limit, including gluon contributions. Our effective action generalizes non-trivially the one obtained for μ_B = 0 by previous authors, and it includes new μ_B -dependent terms. In particular, a topological term μ_B N_B is found, N_B being the baryon number in terms of GB fields with the correct normalization factor. Physical implications of the remaining μ_B -dependent terms are discussed briefly.

ANOMALIES AT FINITE TEMPERATURE AND DENSITY

Chiral anomalies for Abelian and non-Abelian quantum field theories at finite temperature and density (FTFD) are analyzed in detail in both imaginary and real time (IT and RT) formalisms. IT and RT triangle diagrams and IT functional methods (a la Fujikawa) are used at FTFD. The vector anomaly (the one regarding the lepton and baryon numbers) in the Weinberg–Salam theory, for an arbitrary number of fermion families, is also treated using IT functional methods at FTFD. In all cases, the expressions for the FTFD anomalies (as functions of the corresponding quantities) turn out to be identical to those at zero temperature and density, thereby extending previous results by various authors for the finite temperature and zero density case. Moreover, the independence of anomalies from temperature and density is shown to be consistent, at least in the Abelian case, with the analytic continuation from the IT formulation to the RT one.

Exact solution for the Schwinger model at finite temperature

Abstract An exact solution for the Schwinger model at finite temperature is given. Path integral methods and thermo-field dynamics are used. The explicit dependence of the complete propagators with temperature is found.