Botella-Soler, V., Oteo, J. A., Ros, J., & Glendinning, P. (2013). Lyapunov exponent and topological entropy plateaus in piecewise linear maps. J. Phys. A, 46(12), 125101–26pp.
Abstract: We consider a two-parameter family of piecewise linear maps in which the moduli of the two slopes take different values. We provide numerical evidence of the existence of some parameter regions in which the Lyapunov exponent and the topological entropy remain constant. Analytical proof of this phenomenon is also given for certain cases. Surprisingly however, the systems with that property are not conjugate as we prove by using kneading theory.
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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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Casas, F., Oteo, J. A., & Ros, J. (2012). Unitary transformations depending on a small parameter. Proc. R. Soc. A, 468(2139), 685–700.
Abstract: We formulate a unitary perturbation theory for quantum mechanics inspired by the Lie-Deprit formulation of canonical transformations. The original Hamiltonian is converted into a solvable one by a transformation obtained through a Magnus expansion. This ensures unitarity at every order in a small parameter. A comparison with the standard perturbation theory is provided. We work out the scheme up to order ten with some simple examples.
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Modamio, V., Valiente-Dobon, J. J., Jaworski, G., Huyuk, T., Triossi, A., Egea, J., et al. (2015). Digital pulse-timing technique for the neutron detector array NEDA. Nucl. Instrum. Methods Phys. Res. A, 775, 71–76.
Abstract: A new digital pulse-timing algorithm, to be used with the future neutron detector array NEDA, has been developed and tested. The time resolution of four 5 in diameter photomultiplier tubes (XP4512, R4144, R11833-100, and ET9390-kb), coupled to a cylindrical 5 in by 5 in BC501A liquict scintillator detector was measured by employing digital sampling electronics and a constant fraction discriminator (CFD) algorithm. The zero crossing of the CM algorithm was obtained with a cubic spline interpolation, which was continuous up to the second derivative. The performance of the algorithm was studied at sampling rates of 500 MS/s and 200 MS/s. The time resolution obtained with the digital electronics was compared to the values acquired with a standard analog CFD. The result of this comparison shows that the time resolution from the analog and the digital measurements at 500 MS/s and at 200 MS/s are within 15% for all the tested photomultiplier tubes.
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