Two-Dimensional Supersymmetric Quantum Mechanics: Two Fixed Centers of Force

The problem of building supersymmetry in the quantum mechanics of two Coulombian centers of force is analyzed. It is shown that there are essentially two ways of proceeding. The spectral problems of the SUSY (scalar) Hamiltonians are quite similar and become tantamount to solving entangled families of Razavy and Whittaker-Hill equations in the first approach. When the two centers have the same strength, the Whittaker-Hill equations reduce to Mathieu equations. In the second approach, the spectral problems are much more difficult to solve but one can still find the zero-energy ground states.Comment: This is a contribution to the Proc. of the Seventh International Conference ''Symmetry in Nonlinear Mathematical Physics'' (June 24-30, 2007, Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

One-loop mass shift formula for kinks and self-dual vortices

A formula is derived that allows us to compute one-loop mass shifts for kinks and self-dual Abrikosov-Nielsen-Olesen vortices. The procedure is based in canonical quantization and heat kernel/zeta function regularization methods.Comment: LaTex file, 8 pages, 1 figure . Based on a talk given by J. M. G. at the 7th Workshop on Quantum Field Theory under the Influence of External Conditions (QFEXT05), Barcelona, Spain. Minor corrections. Version to appear in Journal of Physics

EPR before EPR: a 1930 Einstein-Bohr thought experiment revisited

In 1930 Einstein argued against consistency of the time-energy uncertainty relation by discussing a thought experiment involving a measurement of mass of the box which emitted a photon. Bohr seemingly triumphed over Einstein by arguing that the Einstein's own general theory of relativity saves the consistency of quantum mechanics. We revisit this thought experiment from a modern point of view at a level suitable for undergraduate readership and find that neither Einstein nor Bohr was right. Instead, this thought experiment should be thought of as an early example of a system demonstrating nonlocal "EPR" quantum correlations, five years before the famous Einstein-Podolsky-Rosen paper.Comment: 11 pages, revised, accepted for publication in Eur. J. Phy

Applying the Minimal Detectable Change of a Static and Dynamic Balance Test Using a Portable Stabilometric Platform to Individually Assess Patients with Balance Disorders

Balance disorders have a high prevalence among elderly people in developed countries, and falls resulting from balance disorders involve high healthcare costs. Therefore, tools and indicators are necessary to assess the response to treatments. Therefore, the aim of this study is to detect relevant changes through minimal detectable change (MDC) values in patients with balance disorders, specifically with vertigo. A test-retest of a static and dynamic balance test was conducted on 34 healthy young volunteer subjects using a portable stabilometric platform. Afterwards, in order to show the MDC applicability, eight patients diagnosed with balance disorders characterized by vertigo of vestibular origin performed the balance test before and after a treatment, contrasting the results with the assessment by a specialist physician. The balance test consisted of four tasks from the Romberg test for static balance control, assessing dynamic postural balance through the limits of stability (LOS). The results obtained in the test-retest show the reproducibility of the system as being similar to or better than those found in the literature. Regarding the static balance variables with the lowest MDC value, we highlight the average velocity of the center of pressure (COP) in all tasks and the root mean square (RMS), the area, and the mediolateral displacement in soft surface, with eyes closed. In LOS, all COP limits and the average speed of the COP and RMS were highlighted. Of the eight patients assessed, an agreement between the specialist physician and the balance test results exists in six of them, and for two of the patients, the specialist physician reported no progression, whereas the balance test showed worsening. Patients showed changes that exceeded the MDC values, and these changes were correlated with the results reported by the specialist physician. We conclude that (at least for these eight patients) certain variables were sufficiently sensitive to detect changes linked to balance progression. This is intended to improve decision making and individualized patient monitoring