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.
|
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.
|
Ibanez-Rosello, B., Bautista-Ballesteros, J. A., Candela-Juan, C., Villaescusa, J. I., Ballester, F., Vijande, J., et al. (2017). Evaluation of the shielding in a treatment room with an electronic brachytherapy unit. J. Radiol. Prot., 37(2), N5–N12.
Abstract: Esteya (R) (Elekta Brachytherapy, Veenendaal, The Netherlands) is an electronic brachytherapy (eBT) system based on a 69.5 kVp x-ray source and a set of collimators of 1 to 3 cm in diameter, used for treating non-melanoma skin cancer lesions. This study aims to estimate room shielding requirements for this unit. The non-primary (scattered and leakage) ambient dose equivalent rates were measured with a Berthold LB-133 monitor (Berthold Technologies, Bad Wildbad, Germany). The latter ranges from 17 mSv h(-1) at 0.25 m distance from the x-ray source to 0.1 mSv h(-1) at 2.5 m. The necessary room shielding was then estimated following US and some European guidelines. The room shielding for all barriers considered was below 2 mmPb. The dose to a companion who, exceptionally, would stay with the patient during all treatment was estimated to be below 1 mSv if a leaded apron is used. In conclusion, Esteya shielding requirements are minimal.
|
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.
|
Pavez, C., Pedreros, J., Tarifeño-Saldivia, A., & Soto, L. (2015). Observation of plasma jets in a table top plasma focus discharge. Phys. Plasmas, 22(4), 040705–5pp.
Abstract: In the last years, medium size Z-pinch experiments operating at tens of kJ are being used to create supersonic plasma jets. Those experiments are produced with wire arrays and radial foils, and they are conducted in generators based on water-filled transmission lines. Also plasma jets have been observed in small X-pinch experiments operating at 1 kJ. In this work, observations of plasma jets produced in a table top plasma focus device by means of optical and digital interferometry are shown. The device was operated at only similar to 70J, achieving 50 kA in 150 ns. The plasma jets were observed after the pinch, in the region close and on the anode, along the axis. The electron density measured from the jets is in the range 10(24)-10(25) m(-3). From two consecutive plasma images separated 18 ns, the axial jet velocity was measured in the order of 4 x 10(4) m/s.
|
