On the propagation of semiclassical Wigner functions

We establish the difference between the propagation of semiclassical Wigner functions and classical Liouville propagation. First we re-discuss the semiclassical limit for the propagator of Wigner functions, which on its own leads to their classical propagation. Then, via stationary phase evaluation of the full integral evolution equation, using the semiclassical expressions of Wigner functions, we provide the correct geometrical prescription for their semiclassical propagation. This is determined by the classical trajectories of the tips of the chords defined by the initial semiclassical Wigner function and centered on their arguments, in contrast to the Liouville propagation which is determined by the classical trajectories of the arguments themselves.Comment: 9 pages, 1 figure. To appear in J. Phys. A. This version matches the one set to print and differs from the previous one (07 Nov 2001) by the addition of two references, a few extra words of explanation and an augmented figure captio

On a nonlocal degenerate parabolic problem

Conditions for the existence and uniqueness of weak solutions for a class of nonlinear nonlocal degenerate parabolic equations are established. The asymptotic behaviour of the solutions as time tends to infinity are also studied. In particular, the finite time extinction and polynomial decay properties are proved

Uniform approximation for the overlap caustic of a quantum state with its translations

The semiclassical Wigner function for a Bohr-quantized energy eigenstate is known to have a caustic along the corresponding classical closed phase space curve in the case of a single degree of freedom. Its Fourier transform, the semiclassical chord function, also has a caustic along the conjugate curve defined as the locus of diameters, i.e. the maximal chords of the original curve. If the latter is convex, so is its conjugate, resulting in a simple fold caustic. The uniform approximation through this caustic, that is here derived, describes the transition undergone by the overlap of the state with its translation, from an oscillatory regime for small chords, to evanescent overlaps, rising to a maximum near the caustic. The diameter-caustic for the Wigner function is also treated.Comment: 14 pages, 9 figure

Um dispositivo analítico de leituras nas ciências da natureza

Objetivo: circunstanciar um dispositivo analítico de leituras em diferentes tipos de discurso relacionados às ciências da natureza. Apoio teórico, com sustentação principal em textos de Eni Orlandi para pressupostos e noções da análise do discurso, tais como: não transparência e materialidade da língua; prioridade para o funcionamento (processo) do discurso, considerado como efeito de sentidos entre locutores; condições deprodução; incompletude do texto; formação discursiva e autoria (repetição: empírica, formal e histórica). A construção do dispositivo analítico consistiu em interpelar com essas noções diferentes tipos de discurso relacionados às ciências da natureza. Entre as conclusões: propor leituras com diferentes tipos de discurso; não hierarquizar as linguagens (comum e matemática) e valorizar a repetição histórica