Vacuum Nodes and Anomalies in Quantum Theories

We show that nodal points of ground states of some quantum systems with magnetic interactions can be identified in simple geometric terms. We analyse in detail two different archetypical systems: i) a planar rotor with a non-trivial magnetic flux $\Phi$, ii) Hall effect on a torus. In the case of the planar rotor we show that the level repulsion generated by any reflection invariant potential $V$ is encoded in the nodal structure of the unique vacuum for $\theta=\pi$. In the second case we prove that the nodes of the first Landau level for unit magnetic charge appear at the crossing of the two non-contractible circles $\alpha_-$, $\beta_-$ with holonomies $h_{\alpha_-}(A)= h_{\beta_-}(A)=-1$ for any reflection invariant potential $V$. This property illustrates the geometric origin of the quantum translation anomaly.Comment: 14 pages, 2 ps-figures, to appear in Commun. Math. Phy

Origin of the anomalies: the modified Heisenberg equation

The origin of the anomalies is analyzed. It is shown that they are due to the fact that the generators of the symmetry do not leave invariant the domain of definition of the Hamiltonian and then a term, normally forgotten in the Heisenberg equation, gives an extra contribution responsible for the non conservation of the charges. This explanation is equivalent to that of the Fujikawa in the path integral formalism. Finally, this approach is applied to the conformal symmetry breaking in two-dimensional quantum mechanics.Comment: 7 pages, LaTe

Influence of Magnetic Field on Effective Electron-Electron Interactions in a Copper Wire

We have measured in a copper wire the energy exchange rate between quasiparticles as a function of the applied magnetic field. We find that the effective electron-electron interaction is strongly modified by the magnetic field, suggesting that magnetic impurities play a role on the interaction processes.Comment: latex anthore.tex, 8 files, 6 figures, 7 pages in: Proceedings of the XXXVIth Rencontres de Moriond `Electronic Correlations: From Meso- to Nano-physics' Les Arcs, France January 20-27, 2001 [SPEC-S01/027

Reciprocal peer tutoring and treatment integrity of elementary school students

Academic concerns are the most common reason students are referred for special services in schools. This obviously leads to the necessity for schools to have secondary prevention services in place to address the needs of students who are struggling. Peer tutoring, in its various forms, has been well documented as an effective and inexpensive intervention for all academic areas. Despite the promise of peer tutoring, research evidence suggests that teachers may not consistently carry out their roles in the peer tutoring process with sufficient accuracy to ensure positive outcomes. One possible solution to this problem is to have a consultant directly monitor the intervention. The purpose of this study was to use the well established procedures of Reciprocal Peer Tutoring and Classwide Peer Tutoring to develop an effective peer tutoring process that can be implemented with an absolute minimum of teacher involvement. Students were responsible for initiating the tutoring sessions, collecting data, evaluating their performances, and administering rewards. Students\u27 work was evaluated and monitored by the consultant rather than the teacher. The results demonstrated that the students implemented the reciprocal peer tutoring procedures with high accuracy and integrity. As a result, the students showed increases in their sight word acquisition. Limitations and future directions are discussed

An Innovative Project to Strengthen and Improve the Knowledge Acquisition in the Degree in Chemistry Using e-Learning Tools

Comunicació presentada a EDULEARN2018, 10th International Conference on Education and New Learning Technologies (July 2-4, 2018, Palma, Mallorca, Spain).The subject "Chemistry II (QU910)" is taught at first academic year (second semester) of the Degree in Chemistry at the University Jaume I. Some of its specific and general competencies are selflearning and writing and oral communication, regarding the main chemical concepts: chemical reactions, elements of the periodic table and calculations of the concentrations of the formed products and the remaining reagents in acid/base, complex, precipitation and redox reactions. We have noticed that 65% of the students have not studied any chemistry subjects (or only one) in High School or Professional Training before undertaking the Degree in Chemistry. The present project aims firstly to help these students to overcome their lack of background, secondly to compare the academic results of the students with and without previous contact with chemistry and finally, to establish actions to solve this prejudicial situation. This objective was reached by the implementation of a zero course, a course including the basic content of chemistry taught in the last years of High School, the month before the beginning of the first academic year. After the first year, students having attended chemistry before university obtained only 0.75/10 points more than the others. The Virtual Classroom, the emails and tutorial played an important role in the achievement of this zero-course

Theory of microwave spectroscopy of Andreev bound states with a Josephson junction

We present a microscopic theory for the current through a tunnel Josephson junction coupled to a non-linear environment, which consists of an Andreev two-level system coupled to a harmonic oscillator. It models a recent experiment [Bretheau, Girit, Pothier, Esteve, and Urbina, Nature (London) 499, 312 (2013)] on photon spectroscopy of Andreev bound states in a superconducting atomic-size contact. We find the eigenenergies and eigenstates of the environment and derive the current through the junction due to inelastic Cooper pair tunneling. The current-voltage characteristic reveals the transitions between the Andreev bound states, the excitation of the harmonic mode that hybridizes with the Andreev bound states, as well as multi-photon processes. The calculated spectra are in fair agreement with the experimental data.Comment: 8 pages, 6 figure