30,457 research outputs found
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
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