Weyl Expansion for Symmetric Potentials

We present a semiclassical expansion of the smooth part of the density of states in potentials with some form of symmetry. The density of states of each irreducible representation is separately evaluated using the Wigner transforms of the projection operators. For discrete symmetries the expansion yields a formally exact but asymptotic series in $\hbar$, while for the rotational $SO(n)$ symmetries the expansion requires averaging over angular momentum as well as energy. A numerical example is given in two dimensions, in which we calculate the leading terms of the Weyl expansion as well as the leading periodic orbit contributions to the symmetry reduced level density.Comment: Four of the five figures are appended as a postscript file. The fifth figure is available by snail mail

Geometric and Diffractive Orbits in the Scattering from Confocal Hyperbolae

We study the scattering resonances between two confocal hyperbolae and show that the spectrum is dominated by the effect of a single periodic orbit. There are two distinct cases depending on whether the orbit is geometric or diffractive. A generalization of periodic orbit theory allows us to incorporate the second possibility. In both cases we also perform a WKB analysis. Although it is found that the semiclassical approximations work best for resonances with large energies and narrow widths, there is reasonable agreement even for resonances with large widths - unlike the two disk scatterer. We also find agreement with the next order correction to periodic orbit theory.Comment: Written in RevTeX. After \end{document} comes a uuencoded .ps file with two figure

Effect of Photobiomodulation on Vinblastine-Poisoned Murine HERS Cells

Objective: The aim of this study was to investigate the effect of near-infrared (NIR) photobiomodulation on the proliferation and glutathione levels in murine Hertwig\u27s epithelial root sheath (HERS) cells after poisoning with vinblastine. Background: Photobiomodulation has been shown to improve wound healing in a number of animal models. There have been no studies on the effect of photobiomodulation on cancer-related chemotherapy injury to the cells that initiate tooth root growth. Materials and Methods: Control groups consisted of murine HERS cells without vinblastine (VB−) and cells with vinblastine at 10, 20, and 30 ng/mL (VB10, VB20, and VB30). Experimental groups consisted of these same groups with light therapy (VB-L, VB10L, VB20L, and VB30L). The cells were exposed to vinblastine for 1 h. Photobiomodulation consisted of a 75-cm2 gallium-aluminum-arsenide light-emitting diode (LED) array at an energy density of 12.8 J/cm2, delivered with 50 mW/cm2 power over 256 s. Results: Vinblastine alone significantly decreased HERS cell proliferation and glutathione levels at all concentrations (VB10 [−55%, p \u3c 1.0 × 10−8]; VB20 [−72%, p \u3c 1.0 × 10−9]; VB30 [−80%, p \u3c 1.0 × 10−10]; and VB10 [−36%, p \u3c 0.0001]; VB20 [−49%, p \u3c 1.0 × 10−6]; VB30 [−53%, p \u3c 1.0 × 10−7] respectively). Photobiomodulation significantly increased cell proliferation at all levels of vinblastine exposure (VB10L [+50%, p \u3c 0.0001]; VB20L [+45%, p \u3c 0.05]; VB30 [+39%, p \u3c 0.05]) but not of the control (+22%, p  = 0.063). The photobiomodulation significantly increased glutathione production in all concentrations of vinblastine except 20 ng/mL (VB10L [+39%, p = 0.007]; VB20L [+19%, p = 0.087]; VB30 [+14%, p = 0.025]) and the control (+12%, p = 0.13). Conclusions: Photobiomodulation demonstrated an improvement in proliferation and glutathione levels in vinblastine-poisoned murine HERS cells