Excitation Spectrum and Correlation Functions of the Z_3-Chiral Potts Quantum Spin Chain

We study the excitation spectrum and the correlation functions of the Z_3- chiral Potts model in the massive high-temperature phase using perturbation expansions and numerical diagonalization. We are mainly interested in results for general chiral angles but we consider also the superintegrable case. For the parameter values considered, we find that the band structure of the low- lying part of the excitation spectrum has the form expected from a quasiparticle picture with two fundamental particles. Studying the N-dependence of the spectrum, we confirm the stability of the second fundamental particle in a limited range of the momentum, even when its energy becomes so high that it lies very high up among the multiparticle scattering states. This is not a phenomenon restricted to the superintegrable line. Calculating a non-translationally invariant correlation function, we give evidence that it is oscillating. Within our numerical accuracy we find a relation between the oscillation length and the dip position of the momentum dispersion of the lightest particle which seems to be quite independent of the chiral angles.Comment: 19 pages + 6 PostScript figures (LaTeX); BONN-TH-94-2

Low-Temperature Expansions and Correlation Functions of the Z_3-Chiral Potts Model

Using perturbative methods we derive new results for the spectrum and correlation functions of the general Z_3-chiral Potts quantum chain in the massive low-temperature phase. Explicit calculations of the ground state energy and the first excitations in the zero momentum sector give excellent approximations and confirm the general statement that the spectrum in the low-temperature phase of general Z_n-spin quantum chains is identical to one in the high-temperature phase where the role of charge and boundary conditions are interchanged. Using a perturbative expansion of the ground state for the Z_3 model we are able to gain some insight in correlation functions. We argue that they might be oscillating and give estimates for the oscillation length as well as the correlation length.Comment: 17 pages (Plain TeX), BONN-HE-93-1

Enhancing the Digital Backchannel Backstage on the Basis of a Formative User Study

Contemporary higher education with its large audiences suffers from passivity of students. Enhancing the classroom with a digital backchannel can contribute to establishing and fostering active participation of and collaboration among students in the lecture. Therefore, we conceived the digital backchannel Backstage specifically tailored for the use in large classes. At an early phase of development we tested its core functionalities in a small-scale user study. The aim of the study was to gain first impressions of its adoption, and also to form a basis for further steps in the conception of Backstage. Regarding adoption we particularly focused on how Backstage influences the participants' questioning behavior, a salient aspect in learning. We observed that during the study much more questions were uttered on Backstage than being asked without backchannel support. Regarding the further development of Backstage we capitalized on the participants' usability feedback. The key of the refinement is the integration of presentation slides in Backstage, which leads to an interesting reconsideration of the user interactions of Backstage

Onsager's algebra and partially orthogonal polynomials

The energy eigenvalues of the superintegrable chiral Potts model are determined by the zeros of special polynomials which define finite representations of Onsager's algebra. The polynomials determining the low-sector eigenvalues have been given by Baxter in 1988. In the Z_3-case they satisfy 4-term recursion relations and so cannot form orthogonal sequences. However, we show that they are closely related to Jacobi polynomials and satisfy a special "partial orthogonality" with respect to a Jacobi weight function.Comment: 8 pages, no figure

Providing guidance on Backstage, a novel digital backchannel for large class teaching

Many articles in the last couple of years argued that it is necessary to promote the active participation of students in lectures with large audiences. One approach to make students actively participate in a lecture is to use a digital backchannel, i.e. a computer-mediated communication platform that allows students to exchange ideas and opinions, without disrupting the lecturer’s discourse. Though, a digital backchannel, in order to be most helpful for learning, have to address the need for guidance of the users interacting. The article presents Backstage, a digital backchannel for large class lectures, and shows how it provides guidance for its users, i.e. the students but also the lecturer. Structural guidance is provided by aligning the usually incoherent backchannel discourse with the presentation slides that are integrated in the backchannel’s user interface. The alignment is thereby asserted by carefully designed backchannel workflows. The article also discusses the guidance of a student’s substantial involvement in both the frontchannel and the backchannel by means of scripts. Through the interactions of guided individuals a social guidance may emerge, leading to a collectively regulated backchannel

Identities in the Superintegrable Chiral Potts Model

We present proofs for a number of identities that are needed to study the superintegrable chiral Potts model in the $Q\ne0$ sector.Comment: LaTeX 2E document, using iopart.cls with iopams packages. 11 pages, uses eufb10 and eurm10 fonts. Typeset twice! vs2: Two equations added. vs3: Introduction adde