Hq(4) symmetry: the linear q-harmonic oscillator based on generalized irreps of the q-deformed Heisenberg algebra

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

THE PARTITION-FUNCTION FOR AN ANYON-LIKE OSCILLATOR

We compute the partition function of an anyon-like harmonic oscillator. The well known results for both the bosonic and fermionic oscillators are then re-obtained as particular cases of our function. The technique we employ is a non-relativistic version of the Green function method used in the computation of one-loop effective actions of quantum field theory.

Circadian rhythm of anti-fungal prenylated chromene in leaves of Piper aduncum

Leaves of Piper aduncum accumulate the anti-fungal chromenes methyl 2,2-dimethyl-2H-1-chromene-6-carboxylate (1) and methyl 2,2-dimethyl-8-(3'-methyl-2'-butenyl)-2H-1-chromene-6-carboxylate (2). The enzymatic formation of 2 from dimethylallyl diphosphate and I was investigated using cell-free extracts of the title plant. An HPLC assay for the prenylation reaction was developed and the enzyme activity measured in the protein extracts. The prenyltransferase that catalyses the transfer of the dimethylallyl group to C-2' of 1 was soluble and required dimethylallyl diphosphate as the prenyl donor. In the leaves, the biosynthesis of the prenylated chromene 2 was time-regulated and prenyltransferase activity depended upon circadian variation. Preliminary characterisation and purification experiments on the prenyltransferase from P. aduncum have been performed. Copyright (C) 2005 John Wiley & Sons, Ltd.

Circadian and seasonal variation in the essential oil from Virola surinamensis leaves

The essential oil from leaves of Virola surinamensis shows circadian variation in elemicin and in monoterpenes during the rainy season (February). The monoterpenes represents 50% of total volatile compounds during the dry season(June). Sesquiterpenes are predominant (50%) in the early rainy season (October). (C) 1997 Published by Elsevier B.V. Ltd.

LARGE-ORDER PERTURBATION EXPANSIONS FOR THE CHARGED HARMONIC-OSCILLATOR

The charged oscillator, defined by the Hamiltonian H = -d2/dr2+ r2 + lambda/r in the domain [0, infinity], is a particular case of the family of spiked oscillators, which does not behave as a supersingular Hamiltonian. This problem is analysed around the three regions lambda --> infinity, lambda --> 0 and lambda --> -infinity by using Rayleigh-Ritz large-order perturbative expansions. A path is found to connect the large lambda regions with the small lambda region by means of the renormalization of the series expansions in lambda. Finally, the Riccati-Pade method is used to construct an implicit expansion around lambda --> 0 which extends to very large values of Absolute value of lambda.

CIRCADIAN OSCILLATORY PATTERNS OF OXYGEN-UPTAKE IN INDIVIDUAL WORKERS OF THE ANT CAMPONOTUS-RUFIPES

Respiratory rates of individual workers of Camponotus rufipes Fabricius (Hymenoptera: Formicidae) were measured at 25-degrees-C and LD 12:12 h (lights on 06.00 hours), DL 12:12 h (lights on 18.00 hours), LL (850 lux) and DD (red light, 20-30 lux), using the micro-Warburg technique. Worker ants were collected from natural nest during the winter of 1987 in a woodland park in the region of Rio Claro, São Paulo, Brazil. The respiration of ants showed a circadian rhythm with acrophase ranging from 20 h 41 min to 01 h 18 min and from 10 h 32 min to 12 h 22 min at LD and DD, respectively. In constant darkness the rhythmometric variables were similar to those presented by ants kept at LD 12:12 h. Under constant light no circadian rhythm in the respiration rates was found. A reduction in the amplitude was observed, indicating an inhibitory effect of this light regime on the respiration process.

Energy localization in the Phi(4) oscillator chain

We study energy localization in a finite one-dimensional Phi(4) oscillator chain with initial energy in a single oscillator of the chain. We numerically calculate the effective number of degrees of freedom sharing the energy on the lattice as a function of time. We find that for energies smaller than a critical value, energy equipartition among the oscillators is reached in a relatively short time. on the other hand, above the critical energy, a decreasing number of particles sharing the energy is observed. We give an estimate of the effective number of degrees of freedom as a function of the energy. Our results suggest that localization is due to the appearance, above threshold, of a breather-like structure. Analytic arguments are given, based on the averaging theory and the analysis of a discrete nonlinear Schrodinger equation approximating the dynamics, to support and explain the numerical results.

Approximate expression for the energy of a D-dimensional anharmonic oscillator

An approximate expression is constructed for the energy of an anharmonic potential with centrifugal barrier. In order to obtain such an analytical expression, the quasi-exact solvability is used and then a fitting of these exact solutions is done.

VARIATIONAL SPIKED OSCILLATOR

A variational analysis of the spiked harmonic oscillator Hamiltonian -d2/dr2 + r2 + lambda/r5/2, lambda > 0, is reported. A trial function automatically satisfying both the Dirichlet boundary condition at the origin and the boundary condition at infinity is introduced. The results are excellent for a very large range of values of the coupling parameter lambda, suggesting that the present variational function is appropriate for the treatment of the spiked oscillator in all its regimes (strong, moderate, and weak interactions).

Nonadiabatic calculations of the oscillator strengths for the helium atom in the hyperspherical adiabatic approach

Energies and wavefunctions are calculated for the bound states of the helium atom in the hyperspherical adiabatic approach by the full inclusion of nonadiabatic couplings. We show that the use of appropriate asymptotic radial boundary conditions not only allows the efficient calculation of energies accurate up to a few ppm for the ground state but also gives increasingly precise results for high-lying excited states with a unique set of equations. The accuracy of the wavefunctions is demonstrated by the calculation of oscillator strengths in the length form for transitions between stares ii S-1(e) and (n + 1) P-1(0) up to n = 29, in agreement with variational calculations.

Perturbative breaking of the pseudospin symmetry in the relativistic harmonic oscillator

We show that relativistic mean fields theories with scalar S, and vector V, quadratic radial potentials can generate a harmonic oscillator with exact pseudospin symmetry and positive energy bound states when S = -V. The eigenenergies are quite different from those of the non-relativistic harmonic oscillator. We also discuss a mechanism for perturbatively breaking this, symmetry by introducing a tensor potential. Our results shed light into the intrinsic relativistic nature of the pseudospin symmetry, which might be important in high density systems such as neutron stars.