Infinite chain of N different deltas: a simple model for a Quantum Wire

We present the exact diagonalization of the Schrodinger operator corresponding to a periodic potential with N deltas of different couplings, for arbitrary N. This basic structure can repeat itself an infinite number of times. Calculations of band structure can be performed with a high degree of accuracy for an infinite chain and of the correspondent eigenlevels in the case of a random chain. The main physical motivation is to modelate quantum wire band structure and the calculation of the associated density of states. These quantities show the fundamental properties we expect for periodic structures although for low energy the band gaps follow unpredictable patterns. In the case of random chains we find Anderson localization; we analize also the role of the eigenstates in the localization patterns and find clear signals of fractality in the conductance. In spite of the simplicity of the model many of the salient features expected in a quantum wire are well reproduced.Comment: 28 pages, LaTeX, 13 eps figures (3 color

Simple model for a Quantum Wire II. Correlations

In a previous paper (Eur. Phys. J. B 30, 239-251 (2002)) we have presented the main features and properties of a simple model which -in spite of its simplicity- describes quite accurately the qualitative behaviour of a quantum wire. The model was composed of N distinct deltas each one carrying a different coupling. We were able to diagonalize the Hamiltonian in the periodic case and yield a complete and analytic description of the subsequent band structure. Furthermore the random case was also analyzed and we were able to describe Anderson localization and fractal structure of the conductance. In the present paper we go one step further and show how to introduce correlations among the sites of the wire. The presence of a correlated disorder manifests itself by altering the distribution of states and the localization of the electrons within the systemComment: RevTex, 7 pages, 9 figures (3 greyscale, 6 coloured

Vacuum Radiation and Symmetry Breaking in Conformally Invariant Quantum Field Theory

The underlying reasons for the difficulty of unitarily implementing the whole conformal group $SO(4,2)$ in a massless Quantum Field Theory (QFT) are investigated in this paper. Firstly, we demonstrate that the singular action of the subgroup of special conformal transformations (SCT), on the standard Minkowski space $M$, cannot be primarily associated with the vacuum radiation problems, the reason being more profound and related to the dynamical breakdown of part of the conformal symmetry (the SCT subgroup, to be more precise) when representations of null mass are selected inside the representations of the whole conformal group. Then we show how the vacuum of the massless QFT radiates under the action of SCT (usually interpreted as transitions to a uniformly accelerated frame) and we calculate exactly the spectrum of the outgoing particles, which proves to be a generalization of the Planckian one, this recovered as a given limit.Comment: 29 pages, Latex, 1 figure, to appear in Commun. Math. Phy

Academic Classrooms and Careers Defined by Race and Gender

The collective classroom and career experiences of a Black woman and White male professor are examined of the last twenty years are examined. It is revealed, that despite the presence of diversity classes and increases in diversity, as regards student and faculty presence, the circumstances of the faculty in this critical examination were defined by the student, faculty, and institutional reactions to their postionalities. Predictably, the White male faculty member had the more positive experiences, while the Black woman’s circumstances were more negative

An explicitly solvable model of the spontaneous PT-symmetry breaking

We contemplate the pair of the purely imaginary delta-function potentials on a finite interval with Dirichlet boundary conditions. The two parameter model exhibits nicely the expected quantitative features of the unavoided level crossing and of a "phase-transition" complexification of the energies. Combining analytic and numerical techniques we investigate strength- and position-dependence of its spectrum.Comment: presented in the int. conference "Pseudo-Hermitian Hamiltonians in Quantum Physics III" (Instanbul, Koc University, June 20 - 22, 2005). accepted in Czechoslovak J. Phy

Race and Adult Education: A Critical Review of the North American Literature

The paper critically evaluates the North American literature showing how race has been treated historically and presents three perspectives on race that inform contemporary research

Adult Education and the Struggle for Knowledge and Power: Practical Action in a Critical Tradition

Along with others we argue that practical space can be found in nearly all forms of adult education for the redistribution of knowledge and power. The purpose of the paper is to describe a way of understanding practical action in a world structured by the inequitable distribution of knowledge and power