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It is explained in which way the ternary symmetric horseshoe can be obtained along a development scenario starting with a binary horseshoe. We explain the case of a complete ternary horseshoe in all detail and then give briefly some further incomplete cases. The key idea is to start with a three degrees of freedom system with a rotational symmetry, reduce the system with the help of the conserved angular momentum to one with two degrees of freedom where the value of the conserved angular momentum acts as a parameter and then let its value go to zero.
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Masculino , Femenino , Humanos , Conducta , Psicoanálisis , Psicología Social , AntropologíaRESUMEN
We present a method for constructing a partition of an incomplete horseshoe in a Poincare map. The partition is based only on the unstable manifolds of the outermost fixed points and eventually their limits. Consequently, this partition becomes natural from the point of view of asymptotic scattering observations. The symbolic dynamics derived from this partition coincides with the one derived from the hierarchical structure of the singularities of the scattering functions.
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We extract the dynamics implicit in an algebraic fitted model Hamiltonian for the deuterium chromophore's vibrational motion in the molecule CDBrClF. The original model has four degrees of freedom, three positions and one representing interbond couplings. A conserved polyad allows in a semiclassical approach the reduction to three degrees of freedom. For most quantum states we can identify the underlying motion that when quantized gives the said state. Most of the classifications, identifications, and assignments are done by visual inspection of the already available wave function semiclassically transformed from the number representation to a representation on the reduced dimension toroidal configuration space corresponding to the classical action and angle variables. The concentration of the wave function density to lower dimensional subsets centered on idealized simple lower dimensional organizing structures and the behavior of the phase along such organizing centers already reveals the atomic motion. Extremely little computational work is needed.
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While Hamiltonians written in terms of position and momentum provide a transparent picture of the motion of a system, Hamiltonians written in terms of Lie algebras are easier to handle quantum mechanically. Therefore we are interested to know how to transform one into the other. Since the exact transformation often leads to complicated expressions, we look for approximations which preserve the essential features. As basic criterion we look for the degree of equality of the classical phase space structures. We illustrate our ideas for the case of two coupled Morse systems and its approximation in terms of the Lie algebra su(2), which is relevant to anharmonic models of molecular spectroscopy. (c) 2001 American Institute of Physics.
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We consider the behavior of open quantum systems through the dependence of the coupling to one decay channel by introducing the coupling parameter alpha, which is proportional to the average degree of overlapping. Under critical conditions, a reorganization of the spectrum takes place that creates a bifurcation of the time scales with respect to the lifetimes of the resonance states. We derive analytically the conditions under which the reorganization process can be understood as a second-order phase transition and illustrate our results by numerical investigations. The conditions are fulfilled, e.g., for a uniform picket-fence level distribution with equal coupling of the states to the continuum. Energy dependencies within the system are included. We consider also the case of an unfolded Gaussian orthogonal ensemble and of a spectrum bounded from below. In all these cases, the reorganization of the spectrum occurs at the critical value alpha(crit) of the control parameter globally over the whole energy range of the spectrum. All states act cooperatively.
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The bioequivalence of three different commercial diazepan tablets (5mg) using the innovator product (Valium, Roche) as a reference was evaluated in eight psychiatric patients, following a multiple-dose regimen (5 mg t.i.d.). Each patient receive the four treatments sequentially according to a Latin square design, with balance for first residual effect. Blood samples were taken once the steady state of the drug had been reached, and the plasma levels were determined using a HPLC method. No statistical differences were found in diazepam steady-state levels after the adminsitration of the four formulations, indicating that they could be aconsidered equivalent