Semiclassical analysis of defect sine-Gordon theory

The classical sine-Gordon model is a two-dimensional integrable field theory, with particle like solutions the so-called solitons. Using its integrability one can define its quantum version without the process of canonical quantization. This bootstrap method uses the fundamental propterties of the model and its quantum features in order to restrict the structure of the scattering matrix as far as possible. The classical model can be extended with integrable discontinuities, purely transmitting jump-defects. Then the quantum version of the extended model can be determined via the bootstrap method again. But the outcoming quantum theory contains the so-called CDD uncertainity. The aim of this article is to carry throw the semiclassical approximation in both the classical and the quantum side of the defect sine-Gordon theory. The CDD ambiguity can be restricted by comparing the two results. The relation between the classical and quantum parameters as well as the resoncances appeared in the spectrum are other objectives

Some aspects of mathematical and chemical modeling of complex chemical processes

Some theoretical questions involved in the mathematical modeling of the kinetics of complex chemical process are discussed. The analysis is carried out for the homogeneous oxidation of ethylbenzene in the liquid phase. Particular attention is given to the determination of the general characteristics of chemical systems from an analysis of mathematical models developed on the basis of linear algebra

Atomic Focusing by Quantum Fields: Entanglement Properties

The coherent manipulation of the atomic matter waves is of great interest both in science and technology. In order to study how an atom optic device alters the coherence of an atomic beam, we consider the quantum lens proposed by Averbukh et al [1] to show the discrete nature of the electromagnetic field. We extend the analysis of this quantum lens to the study of another essentially quantum property present in the focusing process, i.e., the atom-field entanglement, and show how the initial atomic coherence and purity are affected by the entanglement. The dynamics of this process is obtained in closed form. We calculate the beam quality factor and the trace of the square of the reduced density matrix as a function of the average photon number in order to analyze the coherence and purity of the atomic beam during the focusing process.Comment: 10 pages, 4 figure

The Casimir Effect for Parallel Plates Revisited

The Casimir effect for a massless scalar field with Dirichlet and periodic boundary conditions (b.c.) on infinite parallel plates is revisited in the local quantum field theory (lqft) framework introduced by B.Kay. The model displays a number of more realistic features than the ones he treated. In addition to local observables, as the energy density, we propose to consider intensive variables, such as the energy per unit area $\epsilon$, as fundamental observables. Adopting this view, lqft rejects Dirichlet (the same result may be proved for Neumann or mixed) b.c., and accepts periodic b.c.: in the former case $\epsilon$ diverges, in the latter it is finite, as is shown by an expression for the local energy density obtained from lqft through the use of the Poisson summation formula. Another way to see this uses methods from the Euler summation formula: in the proof of regularization independence of the energy per unit area, a regularization-dependent surface term arises upon use of Dirichlet b.c. but not periodic b.c.. For the conformally invariant scalar quantum field, this surface term is absent, due to the condition of zero trace of the energy momentum tensor, as remarked by B.De Witt. The latter property does not hold in tha application to the dark energy problem in Cosmology, in which we argue that periodic b.c. might play a distinguished role.Comment: 25 pages, no figures, late