Botella-Soler, V., Oteo, J. A., & Ros, J. (2012). Coexistence of periods in a bifurcation. Chaos Solitons Fractals, 45(5), 681–686.
Abstract: A particular type of order-to-chaos transition mediated by an infinite set of coexisting neutrally stable limit cycles of different periods is studied in the Varley-Gradwell-Hassell population model. We prove by an algebraic method that this kind of transition can only happen for a particular bifurcation parameter value. Previous results on the structure of the attractor at the transition point are here simplified and extended.
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Blanes, S., Casas, F., Oteo, J. A., & Ros, J. (2010). A pedagogical approach to the Magnus expansion. Eur. J. Phys., 31(4), 907–918.
Abstract: Time-dependent perturbation theory as a tool to compute approximate solutions of the Schrodinger equation does not preserve unitarity. Here we present, in a simple way, how the Magnus expansion (also known as exponential perturbation theory) provides such unitary approximate solutions. The purpose is to illustrate the importance and consequences of such a property. We suggest that the Magnus expansion may be introduced to students in advanced courses of quantum mechanics.
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Baeza-Ballesteros, J., Donini, A., & Nadal-Gisbert, S. (2022). Dynamical measurements of deviations from Newton's 1/r(2) law. Eur. Phys. J. C, 82(2), 154–30pp.
Abstract: In Ref. Donini and Marimon (Eur Phys J C 76:696, arXiv:1609.05654, 2016), an experimental setup aiming at the measurement of deviations from the Newtonian 1/r(2) distance dependence of gravitational interactions was proposed. The theoretical idea behind this setup was to study the trajectories of a “Satellite” with a mass m(S) similar to O(10(-9)) g around a “Planet” with mass m(P) is an element of [10(-7), 10(-5)] g, looking for precession of the orbit. The observation of such feature induced by gravitational interactions would be an unambiguous indication of a gravitational potential with terms different from 1/r and, thus, a powerful tool to detect deviations from Newton's 1/r(2) law. In this paper we optimize the proposed setup in order to achieve maximal sensitivity to look for such Beyond-Newtonian corrections. We then study in detail possible background sources that could induce precession and quantify their impact on the achievable sensitivity. We finally conclude that a dynamical measurement of deviations from newtonianity can test Yukawa-like corrections to the 1/r potential with strength as low as alpha similar to 10(-2) for distances as small as lambda similar to 10 μm.
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Baeza-Ballesteros, J., Donini, A., Molina-Terriza, G., Monrabal, F., & Simon, A. (2024). Towards a realistic setup for a dynamical measurement of deviations from Newton's 1/r2 law: the impact of air viscosity. Eur. Phys. J. C, 84(6), 596–20pp.
Abstract: A novel experimental setup to measure deviations from the 1/r(2) distance dependence of Newtonian gravity was proposed in Donini and Marimon (Eur Phys J C 76:696, 2016). The underlying theoretical idea was to study the orbits of a microscopically-sized planetary system composed of a “Satellite”, with mass m(S) similar to O(10-9) g, and a “Planet”, with mass M-P similar to O(10-5) g at an initial distance of hundreds of microns. The detection of precession of the orbit in this system would be an unambiguous indication of a central potential with terms that scale with the distance differently from 1/r. This is a huge advantage with respect to the measurement of the absolute strength of the attraction between two bodies, as most electrically-induced background potentials do indeed scale as 1/r. Detection of orbit precession is unaffected by these effects, allowing for better sensitivities. In Baeza-Ballesteros et al. (Eur Phys J C 82:154, 2022), the impact of other subleading backgrounds that may induce orbit precession, such as, e.g., the electrical Casimir force or general relativity, was studied in detail. It was found that the proposed setup could test Yukawa-like corrections, alpha x exp(-r/lambda), to the 1/r potential with couplings as low as alpha similar to 10(-2) for distances as small as lambda similar to 10 μm, improving by roughly an order of magnitude present bounds. In this paper, we start to move from a theoretical study of the proposal to a more realistic implementation of the experimental setup. As a first step, we study the impact of air viscosity on the proposed setup and see how the setup should be modified in order to preserve the theoretical sensitivity achieved in Donini and Marimon (2016) and Baeza-Ballesteros et al. (2022).
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Baeza-Ballesteros, J., Hernandez, P., & Romero-Lopez, F. (2022). A lattice study of pi pi scattering at large N-c. J. High Energy Phys., 06(6), 049–39pp.
Abstract: We present the first lattice study of pion-pion scattering with varying number of colors, N-c. We use lattice simulations with four degenerate quark flavors, N-f = 4, and N-c= 3 – 6. We focus on two scattering channels that do not involve vacuum diagrams. These correspond to two irreducible representations of the SU(4) flavor group: the fully symmetric one, SS, and the fully antisymmetric one, AA. The former is a repulsive channel equivalent to the isospin-2 channel of SU(2). By contrast, the latter is attractive and only exists for N-f >= 4. A representative state is (vertical bar D-s(+) pi(+)> – vertical bar D+ K+ >) /root 2. Using Lfischer's formalism, we extract the near-threshold scattering amplitude and we match our results to Chiral Perturbation Theory (ChPT) at large N-c. For this, we compute the analytical U(N-f) ChPT prediction for two-pion scattering, and use the lattice results to constrain the N-c scaling of the relevant low-energy couplings.
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