The SUSY partners of the QES sextic potential revisited

In this paper, the SUSY partner Hamiltonians of the quasi-exactly solvable (QES) sextic potential $V^{\rm qes}(x) = \nu\, x^{6} + 2\, \nu\, \mu\,x^{4} + \left[\mu^2-(4N+3)\nu \right]\, x^{2}$, $N \in \mathbb{Z}^+$, are revisited from a Lie algebraic perspective. It is demonstrated that, in the variable $\tau=x^2$, the underlying $\mathfrak{sl}_2(\mathbb{R})$ hidden algebra of $V^{\rm qes}(x)$ is inherited by its SUSY partner potential $V_1(x)$ only for $N=0$. At fixed $N>0$, the algebraic polynomial operator $h(x,\,\partial_x;\,N)$ that governs the $N$ exact eigenpolynomial solutions of $V_1$ is derived explicitly. These odd-parity solutions appear in the form of zero modes. The potential $V_1$ can be represented as the sum of a polynomial and rational parts. In particular, it is shown that the polynomial component is given by $V^{\rm qes}$ with a different non-integer (cohomology) parameter $N_1=N-\frac{3}{2}$. A confluent second-order SUSY transformation is also implemented for a modified QES sextic potential possessing the energy reflection symmetry. By taking $N$ as a continuous real constant and using the Lagrange-mesh method, highly accurate values ($\sim 20$ s. d.) of the energy $E_n=E_n(N)$ in the interval $N \in [-1,3]$ are calculated for the three lowest states $n=0,1,2$ of the system. The critical value $N_c$ above which tunneling effects (instanton-like terms) can occur is obtained as well. At $N=0$, the non-algebraic sector of the spectrum of $V^{\rm qes}$ is described by means of compact physically relevant trial functions. These solutions allow us to determine the effects in accuracy when the first-order SUSY approach is applied on the level of approximate eigenfunctions.Comment: 25 pages, 20 figure

The Use of "EOF" in the Mean Sea Level Oscillations Study An Application to Cadiz

Oscillation modes in mean sea level in the port of Cadiz are computed and analyzed from simultaneous water level and atmospheric pressure records. Empirical Orthogonal Function Decomposition (EOF), cross spectral and least square harmonic analysis are used. EOF is applied in an unusual way in order to extract common oscillation modes of atmospheric pressure and Mean Sea Level (MSL) series. In spite of the short length of time series, less than four months, EOF is a very powerful tool and makes possible the isolation of astronomical and meteorological oscillation modes

A Simple Method for Tidal Current Prediction in Short Length Convergent Channels An Application to the Vigo and Pontevedra Estuaries

In this paper a simple method for tidal current modelling in short length convergent and elongated channels is presented. The authors have found that for this kind of channels a very suitable approach to tidal current velocity estimation can be obtained through a very simple formula. This method has been developed to obtain reliable tidal current velocity estimations along the channel using as less information as possible. In fact, the only necessary information to apply this method are the harmonic constants of the tidal elevation at any location in the channel and a proper nautical chart. A graphical method is also presented to inquire when the geometrical characteristics of a given channel allow the application of our method. The validation has been performed on two estuaries of the Gallega Estuarine System in Spain

El perfil de clima escolar: estudio transcultural de la validez de una batería de cuestionarios para evaluar el clima escolar

This paper studies the validity of the School Climate Battery of Questionnaires for Secondary and High School Teachers (SCBQSHST). The battery includes five questionnaires: Quality of Leadership, Quality of Teachers' Support, School Motivational Orientation, Quality of Students' Attitude, and Quality of Parental Support. A total of 178 teachers from Costa Rica were compared with 343 Spanish teachers. Confirmatory factor analyses showed that the questionnaires allow assessing teachers' perceptions of the different dimensions of school climate in a valid and reliable way in both Spain and Costa Rica. Differences in the perception of Spanish and Costa Rican teachers about school climate shown by multigroup confirmatory factor analyses are discussed as well as theoretical and practical implications.Este artículo estudia la validez de la Batería de cuestionarios sobre clima escolar para profesores de Secundaria y Bachillerato (BQCE-SB). La batería incluye cinco cuestionarios: calidad de liderazgo, calidad de apoyo docente, orientación motivacional del centro, calidad de las actitudes de los estudiantes y calidad del apoyo de los padres. Un total de 178 docentes de Costa Rica se compararon con 343 docentes españoles. Los análisis factoriales confirmatorios mostraron que los cuestionarios permiten evaluar de manera válida y confiable las percepciones de los docentes sobre las diferentes dimensiones del clima escolar, tanto en España como en Costa Rica. Se discuten las diferencias en la percepción de los docentes españoles y costarricenses sobre el clima escolar que muestran los análisis factoriales confirmatorios multigrupo, así como sus implicaciones teóricas y práctica

Origin of slow magnetic relaxation in Kramers ions with non-uniaxial anisotropy

Transition metal ions with long-lived spin states represent minimum size magnetic bits. Magnetic memory has often been associated with the combination of high spin and strong uniaxial magnetic anisotropy. Yet, slow magnetic relaxation has also been observed in some Kramers ions with dominant easy-plane magnetic anisotropy, albeit only under an external magnetic field. Here we study the spin dynamics of cobalt(II) ions in a model molecular complex. We show, by means of quantitative first-principles calculations, that the slow relaxation in this and other similar systems is a general consequence of time-reversal symmetry that hinders direct spin–phonon processes regardless of the sign of the magnetic anisotropy. Its magnetic field dependence is a subtle manifestation of electronuclear spin entanglement, which opens relaxation channels that would otherwise be forbidden but, at the same time, masks the relaxation phenomenon at zero field. These results provide a promising strategy to synthesize atom-size magnetic memories

Phase diagram of the (bosonic) Double-Exchange Model

The phase diagram of the simplest approximation to Double-Exchange systems, the bosonic Double-Exchange model with antiferromagnetic super-exchange coupling, is fully worked out by means of Monte Carlo simulations, large-N expansions and Variational Mean-Field calculations. We find a rich phase diagram, with no first-order phase transitions. The most surprising finding is the existence of a segment like ordered phase at low temperature for intermediate AFM coupling which cannot be detected in neutron-scattering experiments. This is signaled by a maximum (a cusp) in the specific heat. Below the phase-transition, only short-range ordering would be found in neutron-scattering. Researchers looking for a Quantum Critical Point in manganites should be wary of this possibility. Finite-Size Scaling estimates of critical exponents are presented, although large scaling corrections are present in the reachable lattice sizes.Comment: 17 pages, 14 figure

NICMOS Imaging of Molecular Hydrogen Emission in Seyfert Galaxies

We present NICMOS imaging of broad band and molecular hydrogen emission in Seyfert galaxies. In 6 of 10 Seyferts we detect resolved or extended emission in the 1-0 S(1) 2.121 or 1-0 S(3) 1.9570 micron molecular hydrogen lines. We did not detect emission in the most distant galaxy or in the 2 Seyfert 1 galaxies in our sample because of the luminosity of the nuclear point sources. In NGC 5643, NGC 2110 and MKN 1066, molecular hydrogen emission is detected in the extended narrow line region on scales of a few hundred pc from the nucleus. Emission is coincident with [OIII] and H alpha+[NII] line emission. This emission is also near dust lanes observed in the visible to near-infrared color maps suggesting that a multiphase medium exists near the ionization cones and that the morphology of the line emission is dependent on the density of the ambient media. The high 1-0 S(1) or S(3) H2 to H alpha flux ratio suggests that shock excitation of molecular hydrogen (rather than UV fluorescence) is the dominant excitation process in these extended features. In NGC 2992 and NGC 3227 the molecular hydrogen emission is from 800 and 100 pc diameter `disks' (respectively) which are not directly associated with [OIII] emission and are near high levels of extinction (AV > 10). In NGC 4945 the molecular hydrogen emission appears to be from the edge of a 100 pc superbubble. In these 3 galaxies the molecular gas could be excited by processes associated with local star formation. We confirm previous spectroscopic studies finding that no single mechanism is likely to be responsible for the molecular hydrogen excitation in Seyfert galaxies.Comment: submitted to Ap