arXiv subjects

L. C. Malacarne

Publications and source records attributed to L. C. Malacarne.

25 records · Page 2Linked to original sources

arXiv1999

Path Integral Approach to the Nonextensive Canonical Density Matrix

Feynman's path integral is herein generalized to the nonextensive canonical density matrix based on Tsallis entropy. This generalization is done in two ways by using unnormalized and normalized constraints. Firstly, we consider the path integral formulation with unnormalized constraints, and this generalization is worked out through two different ways, which are shown to be equivalent. These formulations with unnormalized constraints are solutions to two generalized Bloch equations proposed in this work. The first form of the generalized Bloch equation is linear, but with a temperature-dependent effective Hamiltonian; the second form is nonlinear and resembles the anomalous correlated diffusion equation (porous medium equation). Furthermore, we can extend these results to the prescription of field theory using integral representations. The second development is dedicated to analyzing the path integral formulation with normalized constraints. To illustrate the methods introduced here, we analyze the free particle case and a non-interacting scalar field. The results herein obtained are expected to be useful in the discussion of generic nonextensive contexts.

cond-mat.stat-mech↗

arXiv1999

On spin-1 massive particles coupled to a Chern-Simons field

We study spin one particles interacting through a Chern-Simons field. In the Born approximation, we calculate the two body scattering amplitude considering three possible ways to introduce the interaction: (a) a Proca like model minimally coupled to a Chern-Simons field, (b) the model obtained from (a) by replacing the Proca's mass by a Chern-Simons term and (c) a complex Maxwell-Chern-Simons model minimally coupled to a Chern-Simons field. In the low energy regime the results show similarities with the Aharonov-Bohm scattering for spin 1/2 particles. We discuss the one loop renormalization program for the Proca's model. In spite of the bad ultraviolet behavior of the matter field propagator, we show that, up to one loop the model is power counting renormalizable thanks to the Ward identities satisfied by the interaction vertices.

hep-th↗

arXiv1998

On the Nonabelian Aharonov Bohm Scattering of Spinless Particles

The Aharonov Bohm scattering for spinless, isospin 1/2, particles interacting through a nonabelian Chern-Simons field is studied. Starting from the relativistic quantum field theory and using a Coulomb gauge formulation, the one loop renormalization program is implemented. Through the introduction of an intermediary cutoff, separating the regions of high and low integration momentum, the nonrelativistic limit is derived. The next to leading relativistic approximation is also determined. In this approach quantum field theory vacuum polarization effects are automatically incorporated.

hep-th↗

arXiv1998

The Contribution of the Smectic-Nematic Interface to the Surface Energy

The contribution of the smectic-nematic interface to the surface energy of a nematic liquid crystal sample is analyzed. By means of a simple model it is shown that the surface energy depends on the thickness of the region over which the transition smectic-nematic takes place. For perfectly flat substrates this thickness is of the order of the correlation length entering in the transition. An estimate of this contribution shows that it is greater than the one arising from the nematic-substrate interaction. Moreover, it is also shown that the surface energy determined in this way presents a non-monotonic behavior with the temperature.

cond-mat↗

arXiv1998

Quantum Corrections for Generalized Partition Functions

The classical limit for generalized partition functions is obtained using coherent states. In this framework it is presented a general procedure to obtain all the corrections to the classical limit. In particular, the first and second order quantum corrections are worked out explicitly, and the classical limit for the Tsallis thermostatistics is determined. The results of this work generalize the ones obtained by E. Wigner (Phys. Rev. 40 (1932) 749) for usual statistical mechanics.

cond-mat↗

arXiv1998

Perturbation and Variational Methods in Nonextensive Tsallis Statistics

A unified presentation of the perturbation and variational methods for the generalized statistical mechanics based on Tsallis entropy is given here. In the case of the variational method, the Bogoliubov inequality is generalized in a very natural way following the Feynman proof for the usual statistical mechanics. The inequality turns out to be form-invariant with respect to the entropic index $q$. The method is illustrated with a simple example in classical mechanics. The formalisms developed here are expected to be useful in the discussion of nonextensive systems.

cond-mat.stat-mech↗

arXiv1997

On the equivalence of the self-dual and Maxwell-Chern-Simons models coupled to Fermions

We study the exact equivalence between the self-dual model minimally coupled with a Dirac field and the Maxwell-Chern-Simons model with non-minimal magnetic coupling to fermions. We show that the fermion sectors of the models are equivalent only if a Thirring like interaction is included. Using functional methods we verify that, up to renormalizations, the equivalence persists at the quantum level.

hep-th↗