Comment on ``A new efficient method for calculating perturbative energies using functions which are not square integrable'': regularization and justification

The method recently proposed by Skala and Cizek for calculating perturbation energies in a strict sense is ambiguous because it is expressed as a ratio of two quantities which are separately divergent. Even though this ratio comes out finite and gives the correct perturbation energies, the calculational process must be regularized to be justified. We examine one possible method of regularization and show that the proposed method gives traditional quantum mechanics results.Comment: 6 pages in REVTeX, no figure

Generalized Supersymmetric Perturbation Theory

Using the basic ingredient of supersymmetry, we develop a simple alternative approach to perturbation theory in one-dimensional non-relativistic quantum mechanics. The formulae for the energy shifts and wave functions do not involve tedious calculations which appear in the available perturbation theories. The model applicable in the same form to both the ground state and excited bound states, unlike the recently introduced supersymmetric perturbation technique which, together with other approaches based on logarithmic perturbation theory, are involved within the more general framework of the present formalism.Comment: 13 pages article in LaTEX (uses standard article.sty). No Figures. Sent to Ann. Physics (2004

Adaptive homodyne measurement of optical phase

We present an experimental demonstration of the power of real-time feedback in quantum metrology, confirming a theoretical prediction by Wiseman regarding the superior performance of an adaptive homodyne technique for single-shot measurement of optical phase. For phase measurements performed on weak coherent states with no prior knowledge of the signal phase, we show that the variance of adaptive homodyne estimation approaches closer to the fundamental quantum uncertainty limit than any previously demonstrated technique. Our results underscore the importance of real-time feedback for reaching quantum performance limits in coherent telecommunication, precision measurement and information processing.Comment: RevTex4, color PDF figures (separate files), submitted to PR

Distinct mechanisms of Drosophila CRYPTOCHROME-mediated light-evoked membrane depolarization and in vivo clock resetting.

Drosophila CRYPTOCHROME (dCRY) mediates electrophysiological depolarization and circadian clock resetting in response to blue or ultraviolet (UV) light. These light-evoked biological responses operate at different timescales and possibly through different mechanisms. Whether electron transfer down a conserved chain of tryptophan residues underlies biological responses following dCRY light activation has been controversial. To examine these issues in in vivo and in ex vivo whole-brain preparations, we generated transgenic flies expressing tryptophan mutant dCRYs in the conserved electron transfer chain and then measured neuronal electrophysiological phototransduction and behavioral responses to light. Electrophysiological-evoked potential analysis shows that dCRY mediates UV and blue-light-evoked depolarizations that are long lasting, persisting for nearly a minute. Surprisingly, dCRY appears to mediate red-light-evoked depolarization in wild-type flies, absent in both cry-null flies, and following acute treatment with the flavin-specific inhibitor diphenyleneiodonium in wild-type flies. This suggests a previously unsuspected functional signaling role for a neutral semiquinone flavin state (FADH•) for dCRY. The W420 tryptophan residue located closest to the FAD-dCRY interaction site is critical for blue- and UV-light-evoked electrophysiological responses, while other tryptophan residues within electron transfer distance to W420 do not appear to be required for light-evoked electrophysiological responses. Mutation of the dCRY tryptophan residue W342, more distant from the FAD interaction site, mimics the cry-null behavioral light response to constant light exposure. These data indicate that light-evoked dCRY electrical depolarization and clock resetting are mediated by distinct mechanisms

Logarithmic perturbation theory for quasinormal modes

Logarithmic perturbation theory (LPT) is developed and applied to quasinormal modes (QNMs) in open systems. QNMs often do not form a complete set, so LPT is especially convenient because summation over a complete set of unperturbed states is not required. Attention is paid to potentials with exponential tails, and the example of a Poschl-Teller potential is briefly discussed. A numerical method is developed that handles the exponentially large wavefunctions which appear in dealing with QNMs.Comment: 24 pages, 4 Postscript figures, uses ioplppt.sty and epsfig.st

Preliminary Observations on the Effects In Vivo and In Vitro of Low Dose Laser on the Epithelia of the Bladder, Trachea and Tongue of the Mouse

The effects of low dose CW laser were studied by in vivo and in vitro systems. The experimental tissues that were used included bladders, tracheas and tongues as experimental tissues. Buddings (round surface projections) from the transitional epithelium of bladder were frequently observed 3 days after laser treatment in both in vivo and in vitro systems. The trachea and tongue were less affected. In both the in vivo and in vitro systems, some epithelial cells of the trachea showed decreased microvilli and cilia 3 days after treatment whereas the epithelial cells of the tongue revealed no response to laser treatment in both systems. Low dose laser, however, appeared to promote the rate of healing of experimental tongue ulcer: healing was about 1 day earlier in the laser treated than non-treated animals and vessel infiltration and epithelialization were detected earlier in the treated

Developmental dyscalculia and low numeracy in Chinese children

Children struggle with mathematics for different reasons. Developmental dyscalculia and low numeracy - two kinds of mathematical difficulties - may have their roots, respectively, in poor understanding of exact non-symbolic numerosities and of symbolic numerals. This study was the first to explore whether Chinese children, despite cultural and linguistic factors supporting their mathematical learning, also showed such mathematical difficulties and whether such difficulties have measurable impact on children's early school mathematical performance. First-graders, classified as dyscalculia, low numeracy, or normal achievement, were compared for their performance in various school mathematical tasks requiring a grasp of non-symbolic numerosities (i.e., non-symbolic tasks) or an understanding of symbolic numerals (i.e., symbolic tasks). Children with dyscalculia showed poorer performance than their peers in non-symbolic tasks but not symbolic ones, whereas those with low numeracy showed poorer performance in symbolic tasks but not non-symbolic ones. As hypothesized, these findings suggested that dyscalculia and low numeracy were distinct deficits and caused by deficits in non-symbolic and symbolic processing, respectively. These findings went beyond prior research that only documented generally low mathematical achievements for these two groups of children. Moreover, these deficits appeared to be persistent and could not be remedied simply through day-to-day school mathematical learning. The present findings highlighted the importance of tailoring early learning support for children with these distinct deficits, and pointed to future directions for the screening of such mathematical difficulties among Chinese children. © 2013 Elsevier Ltd.postprin