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See detailSemiclassical theory for transmission through open billiards: Convergence towards quantum transport
Wirtz, Ludger UL; Stampfer, C.; Rotter, S. et al

in Physical Review. E. (2003), 67(1),

We present a semiclassical theory for transmission through open quantum billiards which converges towards quantum transport. The transmission amplitude can be expressed as a sum over all classical paths ... [more ▼]

We present a semiclassical theory for transmission through open quantum billiards which converges towards quantum transport. The transmission amplitude can be expressed as a sum over all classical paths and pseudopaths which consist of classical path segments joined by "kinks," i.e., diffractive scattering at lead mouths. For a rectangular billiard we show numerically that the sum over all such paths with a given number of kinks K converges to the quantum transmission amplitude as K-->infinity. Unitarity of the semiclassical theory is restored as K approaches infinity. Moreover, we find excellent agreement with the quantum path-length power spectrum up to very long path length. [less ▲]

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See detailOptical and x-ray evidence of the de vries sm-A*-sm-C* transition in a non-layer shrinkage ferroelectric liquid crystal with very weak interlayer tilt correlation
Lagerwall, Jan UL; Giesselmann, Frank; Radcliffe, M. D.

in Physical Review. E. (2002), 66(3), 031703

A non-layer-shrinkage fluorinated ferroelectric liquid crystal compound, 8422@2F3\#, has been characterized by means of optical, x-ray, and calorimetric methods. The orientational distribution within ... [more ▼]

A non-layer-shrinkage fluorinated ferroelectric liquid crystal compound, 8422@2F3\#, has been characterized by means of optical, x-ray, and calorimetric methods. The orientational distribution within macroscopic volumes determined through wide-angle x-ray scattering and birefringence measurements, was found to be identical in the Sm-A* and helical Sm-C* phases. Together with the absence of layer shrinkage, this constitutes strong evidence that the second-order Sm-A*–Sm-C* transition in this material is well described by the diffuse cone model of de Vries. The absolute values of the layer spacing show that the molecules aggregate to antiparallel pairs. The molecular interaction across the layer boundaries will then occur only between fluorine atoms, leading to unusually weak interlayer tilt direction correlation. This explains the experimental observations of a very easily disturbed Sm-C* helix and a peculiar surface-stabilized texture. Tilt angle and birefringence values as a function of field and temperature have been evaluated in the Sm-A* and Sm-C* phases and the results corroborate the conclusions from the x-ray investigations. [less ▲]

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