Semiclassical energy formulas for power-law and log potentials in quantum mechanics

We study a single particle which obeys non-relativistic quantum mechanics in R^N and has Hamiltonian H = -Delta + V(r), where V(r) = sgn(q)r^q. If N \geq 2, then q > -2, and if N = 1, then q > -1. The discrete eigenvalues E_{n\ell} may be represented exactly by the semiclassical expression E_{n\ell}(q) = min_{r>0}\{P_{n\ell}(q)^2/r^2+ V(r)}. The case q = 0 corresponds to V(r) = ln(r). By writing one power as a smooth transformation of another, and using envelope theory, it has earlier been proved that the P_{n\ell}(q) functions are monotone increasing. Recent refinements to the comparison theorem of QM in which comparison potentials can cross over, allow us to prove for n = 1 that Q(q)=Z(q)P(q) is monotone increasing, even though the factor Z(q)=(1+q/N)^{1/q} is monotone decreasing. Thus P(q) cannot increase too slowly. This result yields some sharper estimates for power-potential eigenvlaues at the bottom of each angular-momentum subspace.Comment: 20 pages, 5 figure

Cartilage on the Move: Cartilage Lineage Tracing During Tadpole Metamorphosis

The reorganization of cranial cartilages during tadpole metamorphosis is a set of complex processes. The fates of larval cartilage-forming cells (chondrocytes) and sources of adult chondrocytes are largely unknown. Individual larval cranial cartilages may either degenerate or remodel, while many adult cartilages appear to form de novo during metamorphosis. Determining the extent to which adult chondrocytes/cartilages are derived from larval chondrocytes during metamorphosis requires new techniques in chondrocyte lineage tracing. We have developed two transgenic systems to label cartilage cells throughout the body with fluorescent proteins. One system strongly labels early tadpole cartilages only. The other system inducibly labels forming cartilages at any developmental stage. We examined cartilages of the skull (viscero- and neurocranium), and identified larval cartilages that either resorb or remodel into adult cartilages. Our data show that the adult otic capsules, tecti anterius and posterius, hyale, and portions of Meckel\u27s cartilage are derived from larval chondrocytes. Our data also suggest that most adult cartilages form de novo, though we cannot rule out the potential for extreme larval chondrocyte proliferation or de- and re-differentiation, which could dilute our fluorescent protein signal. The transgenic lineage tracing strategies developed here are the first examples of inducible, skeleton-specific, lineage tracing in Xenopus

Coherent states on spheres

We describe a family of coherent states and an associated resolution of the identity for a quantum particle whose classical configuration space is the d-dimensional sphere S^d. The coherent states are labeled by points in the associated phase space T*(S^d). These coherent states are NOT of Perelomov type but rather are constructed as the eigenvectors of suitably defined annihilation operators. We describe as well the Segal-Bargmann representation for the system, the associated unitary Segal-Bargmann transform, and a natural inversion formula. Although many of these results are in principle special cases of the results of B. Hall and M. Stenzel, we give here a substantially different description based on ideas of T. Thiemann and of K. Kowalski and J. Rembielinski. All of these results can be generalized to a system whose configuration space is an arbitrary compact symmetric space. We focus on the sphere case in order to be able to carry out the calculations in a self-contained and explicit way.Comment: Revised version. Submitted to J. Mathematical Physic

On the Theory of Killing Orbits in Space-Time

This paper gives a theoretical discussion of the orbits and isotropies which arise in a space-time which admits a Lie algebra of Killing vector fields. The submanifold structure of the orbits is explored together with their induced Killing vector structure. A general decomposition of a space-time in terms of the nature and dimension of its orbits is given and the concept of stability and instability for orbits introduced. A general relation is shown linking the dimensions of the Killing algebra, the orbits and the isotropies. The well-behaved nature of "stable" orbits and the possible miss-behaviour of the "unstable" ones is pointed out and, in particular, the fact that independent Killing vector fields in space-time may not induce independent such vector fields on unstable orbits. Several examples are presented to exhibit these features. Finally, an appendix is given which revisits and attempts to clarify the well-known theorem of Fubini on the dimension of Killing orbits.Comment: Latex, 19 pages, no figur

Supersymmetry, local horizontal unification, and a solution to the flavor puzzle

Supersymmetric gauge models with local horizontal symmetries are known to generate large flavor changing neutral current effects induced by supersymmetry breaking D-terms. We show how the presence of a U(1) gauge symmetry solves this problem. We then construct a realistic gauge model with SU(2)_H x U(1)_H as the local horizontal symmetry and suggest that the U(1)_H factor may be identified with the anomalous U(1) induced by string compactification. This model explains the observed hierarchies among the quark masses and mixing angles, accommodates naturally the solar and atmospheric neutrino data, and provides simultaneously a solution to the supersymmetric flavor problem. The model can be excluded if the rare decay \mu --> e \gamma is not observed in the current round of experiments.Comment: 10 pages in RevTe

High-fat meals rich in EPA plus DHA compared with DHA only have differential effects on postprandial lipemia and plasma 8-isoprostane F-2 alpha concentrations relative to a control high-oleic acid meal: a randomized controlled trial

Background: Eicosapentaenoic acid (EPA) plus docosahexaenoic acid (DHA) supplementation has beneficial cardiovascular effects, but postprandial influences of these individual fatty acids are unclear. Objectives: The primary objective was to determine the vascular effects of EPA + DHA compared with DHA only during postprandial lipemia relative to control high–oleic acid meals; the secondary objective was to characterize the effects of linoleic acid–enriched high-fat meals relative to the control meal. Design: We conducted a randomized, controlled, double-blind crossover trial of 4 high-fat (75-g) meals containing 1) high–oleic acid sunflower oil (HOS; control), 2) HOS + fish oil (FO; 5 g EPA and DHA), 3) HOS + algal oil (AO; 5 g DHA), and 4) high–linoleic acid sunflower oil (HLS) in 16 healthy men (aged 35–70 y) with higher than optimal fasting triacylglycerol concentrations (mean ± SD triacylglycerol, 1.9 ± 0.5 mmol/L). Results: Elevations in triacylglycerol concentration relative to baseline were slightly reduced after FO and HLS compared with the HOS control (P < 0.05). The characteristic decrease from baseline in plasma nonesterified fatty acids after a mixed meal was inhibited after AO (Δ 0–3 h, P < 0.05). HLS increased the augmentation index compared with the other test meals (P < 0.05), although the digital volume pulse–reflection index was not significantly different. Plasma 8-isoprostane F(2α) analysis revealed opposing effects of FO (increased) and AO (reduced) compared with the control (P < 0.05). No differences in nitric oxide metabolites were observed. Conclusions: These data show differential postprandial 8-isoprostane F(2α) responses to high-fat meals containing EPA + DHA–rich fish oil compared with DHA-rich AO, but these differences were not associated with consistent effects on postprandial vascular function or lipemia. More detailed analyses of polyunsaturated fatty acid–derived lipid mediators are required to determine possible divergent functional effects of single meals rich in either DHA or EPA. This trial was registered at clinicaltrials.gov as NCT01618071

Hemoglobin genotype has minimal influence on the physiological response of juvenile atlantic cod (Gadus morhua) to environmental challenges

Hemoglobin (Hb) polymorphism in cod is associated with temperature‐related differences in biogeographical distribution, and several authors have suggested that functional characteristics of the various hemoglobin isoforms (HbIs) directly influence phenotypic traits such as growth rate. However, no study has directly examined whether Hb genotype translates into physiological differences at the whole animal level. Thus, we generated a family of juvenile Atlantic cod consisting of all three main Hb genotypes (HbI‐1/1, HbI‐2/2, and HbI‐1/2) by crossing a single pair of heterozygous parents, and we compared their metabolic and cortisol responses to an acute thermal challenge (10&deg;C to their critical thermal maximum [CTM] or 22&deg;C, respectively) and tolerance of graded hypoxia. There were no differences in routine metabolism (at 10&deg;C), maximum metabolic rate, metabolic scope, CTM (overall mean 22.9&deg; &plusmn; 0.2&deg;C), or resting and poststress plasma cortisol levels among Hb genotypes. Further, although the HbI‐1/1 fish grew more (by 15%&ndash;30% during the first 9 mo) when reared at 10&deg; &plusmn; 1&deg;C and had a slightly enhanced hypoxia tolerance at 10&deg;C (e.g., the critical O2 levels for HbI‐1/1, HbI‐2/2, and HbI‐1/2 cod were 35.56% &plusmn; 1.24%, and 40.20% &plusmn; 1.99% air saturation, respectively), these results are contradictory to expectations based on HbI functional properties. Thus, our findings (1) do not support previous assumptions that growth rate differences among cod Hb genotypes result from a more efficient use of the oxygen supply&mdash;that is, reduced standard metabolic rates and/or increased metabolic capacity&mdash;and (2) suggest that in juvenile cod, there is no selective advantage to having a particular Hb genotype with regards to the capacity to withstand ecologically relevant environmental challenges.<br /

Comment on 'Non-equilibrium thermodynamics of light absorption'

A recent paper by Meszéna and Westerhoff (1999 J. Phys. A: Math. Gen. 32 301) has aimed to address what is referred to as a principal question of biological thermodynamics, the possibility of describing photosynthesis in terms of non-equilibrium thermodynamics. The issue is associated with a misrepresentation of the fundamental photophysics involved, and as a result the analysis is invalid

Coherent states for compact Lie groups and their large-N limits

The first two parts of this article surveys results related to the heat-kernel coherent states for a compact Lie group K. I begin by reviewing the definition of the coherent states, their resolution of the identity, and the associated Segal-Bargmann transform. I then describe related results including connections to geometric quantization and (1+1)-dimensional Yang--Mills theory, the associated coherent states on spheres, and applications to quantum gravity. The third part of this article summarizes recent work of mine with Driver and Kemp on the large-N limit of the Segal--Bargmann transform for the unitary group U(N). A key result is the identification of the leading-order large-N behavior of the Laplacian on "trace polynomials."Comment: Submitted to the proceeding of the CIRM conference, "Coherent states and their applications: A contemporary panorama.