6,859 research outputs found
Quasi-exact solvability beyond the SL(2) algebraization
We present evidence to suggest that the study of one dimensional
quasi-exactly solvable (QES) models in quantum mechanics should be extended
beyond the usual \sla(2) approach. The motivation is twofold: We first show
that certain quasi-exactly solvable potentials constructed with the \sla(2)
Lie algebraic method allow for a new larger portion of the spectrum to be
obtained algebraically. This is done via another algebraization in which the
algebraic hamiltonian cannot be expressed as a polynomial in the generators of
\sla(2). We then show an example of a new quasi-exactly solvable potential
which cannot be obtained within the Lie-algebraic approach.Comment: Submitted to the proceedings of the 2005 Dubna workshop on
superintegrabilit
The 3s Rydberg state as a doorway state in the ultrafast dynamics of 1,1-difluoroethylene
The deactivation dynamics of 1,1-difluoroethylene after light excitation is studied within the surface hopping formalism in the presence of 3s and 3p Rydberg states using multi-state second order perturbation theory (MS-CASPT2). Due to the proximity of the Rydberg π-3s state with the ππ* state, the states are mixed favoring ultrafast exchange of population via a conical intersection that closely resembles the equilibrium structure. After excitation, it is found that the π-3s state acts as a doorway state, trapping the population and delaying internal conversion to the ππ* state, from which deactivation to the closed-shell ground state takes place. Besides the conical intersection between the π-3s and ππ* states, five additional conical intersections between the ππ* state and the ground state are found, indicating that after the system is excited, it stretches the C[double bond, length as m-dash]C bond before it twists and pyramidalizes at any of the carbon atoms, in the spirit of a hula-twist mechanism
Tunable entanglement distillation of spatially correlated down-converted photons
We report on a new technique for entanglement distillation of the bipartite
continuous variable state of spatially correlated photons generated in the
spontaneous parametric down-conversion process (SPDC), where tunable
non-Gaussian operations are implemented and the post-processed entanglement is
certified in real-time using a single-photon sensitive electron multiplying CCD
(EMCCD) camera. The local operations are performed using non-Gaussian filters
modulated into a programmable spatial light modulator and, by using the EMCCD
camera for actively recording the probability distributions of the
twin-photons, one has fine control of the Schmidt number of the distilled
state. We show that even simple non-Gaussian filters can be finely tuned to a
~67% net gain of the initial entanglement generated in the SPDC process.Comment: 12 pages, 6 figure
Promoting healthy lifestyle habits through learning based on active video games
The overweight and obesity have been declared as a worldwide health problem. Active videogames and technologies can be used as attractive tools to support educational interventions with children. Thus, in this paper, we present an educational program to promote healthy habits in children with obesity using active videogames and motor play as main strategies. This program was developed with 46 children and their parents in collaboration with the hospital and schools. The results show positive effects in the knowledge about healthy habits and behaviors of children
Riemann Surfaces of genus g with an automorphism of order p prime and p>g
The present work completes the classification of the compact Riemann surfaces
of genus g with an analytic automorphism of order p (prime number) and p > g.
More precisely, we construct a parameteriza- tion space for them, we compute
their groups of uniformization and we compute their full automorphism groups.
Also, we give affine equations for special cases and some implications on the
components of the singular locus of the moduli space of smooth curves of genus
g.Comment: 28 pages, 5 figure
A conjecture on Exceptional Orthogonal Polynomials
Exceptional orthogonal polynomial systems (X-OPS) arise as eigenfunctions of
Sturm-Liouville problems and generalize in this sense the classical families of
Hermite, Laguerre and Jacobi. They also generalize the family of CPRS
orthogonal polynomials. We formulate the following conjecture: every
exceptional orthogonal polynomial system is related to a classical system by a
Darboux-Crum transformation. We give a proof of this conjecture for codimension
2 exceptional orthogonal polynomials (X2-OPs). As a by-product of this
analysis, we prove a Bochner-type theorem classifying all possible X2-OPS. The
classification includes all cases known to date plus some new examples of
X2-Laguerre and X2-Jacobi polynomials
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