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

Estimation of the mechanical properties of the eye through the study of its vibrational modes

Measuring the eye's mechanical properties in vivo and with minimally invasive techniques can be the key for individualized solutions to a number of eye pathologies. The development of such techniques largely relies on a computational modelling of the eyeball and, it optimally requires the synergic interplay between experimentation and numerical simulation. In Astrophysics and Geophysics the remote measurement of structural properties of the systems of their realm is performed on the basis of (helio-)seismic techniques. As a biomechanical system, the eyeball possesses normal vibrational modes encompassing rich information about its structure and mechanical properties. However, the integral analysis of the eyeball vibrational modes has not been performed yet. Here we develop a new finite difference method to compute both the spheroidal and, specially, the toroidal eigenfrequencies of the human eye. Using this numerical model, we show that the vibrational eigenfrequencies of the human eye fall in the interval 100 Hz - 10 MHz. We find that compressible vibrational modes may release a trace on high frequency changes of the intraocular pressure, while incompressible normal modes could be registered analyzing the scattering pattern that the motions of the vitreous humour leave on the retina. Existing contact lenses with embebed devices operating at high sampling frequency could be used to register the microfluctuations of the eyeball shape we obtain. We advance that an inverse problem to obtain the mechanical properties of a given eye (e.g., Young's modulus, Poisson ratio) measuring its normal frequencies is doable. These measurements can be done using non-invasive techniques, opening very interesting perspectives to estimate the mechanical properties of eyes in vivo. Future research might relate various ocular pathologies with anomalies in measured vibrational frequencies of the eye.Comment: Published in PLoS ONE as Open Access Research Article. 17 pages, 5 color figure

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

Divisive Normalization from Wilson-Cowan Dynamics

Divisive Normalization and the Wilson-Cowan equations are influential models of neural interaction and saturation [Carandini and Heeger Nat.Rev.Neurosci. 2012; Wilson and Cowan Kybernetik 1973]. However, they have not been analytically related yet. In this work we show that Divisive Normalization can be obtained from the Wilson-Cowan model. Specifically, assuming that Divisive Normalization is the steady state solution of the Wilson-Cowan differential equation, we find that the kernel that controls neural interactions in Divisive Normalization depends on the Wilson-Cowan kernel but also has a signal-dependent contribution. A standard stability analysis of a Wilson-Cowan model with the parameters obtained from our relation shows that the Divisive Normalization solution is a stable node. This stability demonstrates the consistency of our steady state assumption, and is in line with the straightforward use of Divisive Normalization with time-varying stimuli. The proposed theory provides a physiological foundation (a relation to a dynamical network with fixed wiring among neurons) for the functional suggestions that have been done on the need of signal-dependent Divisive Normalization [e.g. in Coen-Cagli et al., PLoS Comp.Biol. 2012]. Moreover, this theory explains the modifications that had to be introduced ad-hoc in Gaussian kernels of Divisive Normalization in [Martinez et al. Front. Neurosci. 2019] to reproduce contrast responses. The proposed relation implies that the Wilson-Cowan dynamics also reproduces visual masking and subjective image distortion metrics, which up to now had been mainly explained via Divisive Normalization. Finally, this relation allows to apply to Divisive Normalization the methods which up to now had been developed for dynamical systems such as Wilson-Cowan networks

Management of diversity in master classroom: an increasing challenge for science education in valencian universities

Comunicació presentada a INTED2018, 12th International Technology, Education and Development Conference. (March 5-7, 2018, Valencia, Spain).Currently, many foreign students study a Master degree at the Valencian Universities. We can find students, which have immigrated to Spain in the recent years, and then have partially or fully follow the Spanish curricula (High School and/or Grade), and others which have come specifically to study the Master, attracted by the reputation of the Universities and the job and way-of-life offered by the country, and then have achieved their Grade in their countries. This has increased the diversity of the students in the classrooms, related to the ethnic origin, mother language, study practices, background and integration in the society. The present work gives an overview on how students and teacher manage the heterogeneity and diversity in a Master classroom related to chemistry. The term “diversity” is first detailed prior to discussing explicit studies. Different aspects of diversity are stated. The personal experience of the foreign students to adapt to the Spanish courses and environment was investigated. The actions taken by the lecturer to take advantage of diversity and minimize its negative effects were examined. A comparison between the academic results obtained by international and national students is given. Finally, the attention will be focused on language, study practices and background, since these dimensions are frequently discussed in the Valencian context. The implications and opportunities that offer diversity for national but also for international science research are presented

Design of the laboratory script by the students in chemistry practicals: Analysis of water

Comunicació presentada a INTED2018, 12th International Technology, Education and Development Conference. (March 5-7, 2018, Valencia, Spain).The laboratory practices during the Degree in Chemistry are currently designed so that the student must learn and execute a fully developed experimental protocol, previously written up by the professor, which contains all the information and requirements for the correct development of each laboratory session. Under these conditions, students do not need to take any initiative and, consequently, they do not put enough effort in reaching practical abilities with a well-based scientific criterion and do not try to think over the purpose of each lab operation, as well as the reason to use each material and/or each reagent. Thus, with the aim to promote a more active role of the students in their learning process and to improve their autonomy, a new laboratory practices design has been developed in this work, which follows methodologies on project-based cooperative learning: the students have been requested to elaborate themselves the laboratory script by pairs. With this innovative design, we pursue to involve the students in both elaboration and execution steps of the laboratory practicals, and then to increase their attention on them. Besides, the required bibliographic research would improve their knowledge about the studied topic and all aspects about the work at the laboratory. The practicals to-be-developed were related to the study of the physico-chemical quality of natural water, which has a high social relevance

Electron transport through a metal-molecule-metal junction

Molecules of bisthiolterthiophene have been adsorbed on the two facing gold electrodes of a mechanically controllable break junction in order to form metal-molecule(s)-metal junctions. Current-voltage (I-V) characteristics have been recorded at room temperature. Zero bias conductances were measured in the 10-100 nS range and different kinds of non-linear I-V curves with step-like features were reproducibly obtained. Switching between different kinds of I-V curves could be induced by varying the distance between the two metallic electrodes. The experimental results are discussed within the framework of tunneling transport models explicitly taking into account the discrete nature of the electronic spectrum of the molecule.Comment: 12 pages, 12 figures to appear in Phys. Rev. B 59(19) 199

Multi-mode storage and retrieval of microwave fields in a spin ensemble

A quantum memory at microwave frequencies, able to store the state of multiple superconducting qubits for long times, is a key element for quantum information processing. Electronic and nuclear spins are natural candidates for the storage medium as their coherence time can be well above one second. Benefiting from these long coherence times requires to apply the refocusing techniques used in magnetic resonance, a major challenge in the context of hybrid quantum circuits. Here we report the first implementation of such a scheme, using ensembles of nitrogen-vacancy (NV) centres in diamond coupled to a superconducting resonator, in a setup compatible with superconducting qubit technology. We implement the active reset of the NV spins into their ground state by optical pumping and their refocusing by Hahn echo sequences. This enables the storage of multiple microwave pulses at the picoWatt level and their retrieval after up to $35 \mu$s, a three orders of magnitude improvement compared to previous experiments.Comment: 8 pages, 5 figures + Supplementary information (text and 6 figures