A Solvable Model for Decoupling of Interacting Clusters

We consider M clusters of interacting particles, whose in-group interactions are arbitrary, and inter-group interactions are approximated by oscillator potentials. We show that there are masses and frequencies that decouple the in-group and inter-group degrees of freedom, which reduces the initial problem to M independent problems that describe each of the relative in-group systems. The dynamics of the M center-of-mass coordinates is described by the analytically solvable problem of M coupled harmonic oscillators. This paper derives and discusses these decoupling conditions. Furthermore, to illustrate our findings, we consider a charged impurity interacting with a ring of ions. We argue that the impurity can be used to probe the center-of-mass dynamics of the ions.Comment: Version accepted for publication in EP

Poincare Semigroup Symmetry as an Emergent Property of Unstable Systems

The notion that elementary systems correspond to irreducible representations of the Poincare group is the starting point for this paper, which then goes on to discuss how a semigroup for the time evolution of unstable states and resonances could emerge from the underlying Poincare symmetry. Important tools in this analysis are the Clebsch-Gordan coefficients for the Poincare group.Comment: 17 pages, 1 figur

Testing the test: item response curves and test quality

We present a simple technique for evaluating multiple-choice questions and their answers beyond the usual measures of difficulty and the effectiveness of distractors. The technique involves the construction and qualitative consideration of item response curves and is based on item response theory from the field of education measurement. To demonstrate the technique, we apply item response curve analysis to three questions from the Force Concept Inventory. Item response curve analysis allows us to characterize qualitatively whether these questions are efficient, where efficient is defined in terms of the construction, performance, and discrimination of a question and its answer choices. This technique can be used to develop future multiple-choice examination questions and a better understanding of results from existing diagnostic instruments