Maslov indices and monodromy

We prove that for a Hamiltonian system on a cotangent bundle that is Liouville-integrable and has monodromy the vector of Maslov indices is an eigenvector of the monodromy matrix with eigenvalue 1. As a corollary the resulting restrictions on the monodromy matrix are derived

Semiclassical Trace Formulas for Noninteracting Identical Particles

We extend the Gutzwiller trace formula to systems of noninteracting identical particles. The standard relation for isolated orbits does not apply since the energy of each particle is separately conserved causing the periodic orbits to occur in continuous families. The identical nature of the particles also introduces discrete permutational symmetries. We exploit the formalism of Creagh and Littlejohn [Phys. Rev. A 44, 836 (1991)], who have studied semiclassical dynamics in the presence of continuous symmetries, to derive many-body trace formulas for the full and symmetry-reduced densities of states. Numerical studies of the three-particle cardioid billiard are used to explicitly illustrate and test the results of the theory.Comment: 29 pages, 11 figures, submitted to PR

SERUM LUTEINIZING HORMONE AND FOLLICLE STIMULATING HORMONE IN NORMAL CHILDREN AND PATIENTS WITH VARIOUS CLINICAL DISORDERS

Serum concentrations of luteinizing hormone (LH) and follicle stimulating hormone (FSH) were determined in 329 normal children and 185 individuals with endocrinological abnormalities or variations of development. A significant increase of gonadotrophins is noted at the onset of puberty among the boys and at menarche for girls. The values are compared with serum concentrations of LH and FSH in children with abnormalities of sexual development, pituitary malfunction as well as other clinical abnormalities. Comparable levels for age and stage of development were found for premature thelarche, premature adrenarche, cryptorchidism, male pseudohermaphroditism and pubertal gynaecomastia. Hypogonadal individuals (Klinefelter's and Turner's syndrome, pure ovarian dysgenesis and testicular dysgenesis) have markedly elevated values while those with pituitary hypofunction had low values. Patients with sexual prococity tended to have elevated concentrations.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73601/1/j.1365-2265.1973.tb00427.x.pd

Isolation predicts compositional change after discrete disturbances in a global meta-study

Globally, anthropogenic disturbances are occurring at unprecedented rates and over extensive spatial and temporal scales. Human activities also affect natural disturbances, prompting shifts in their timing and intensities. Thus, there is an urgent need to understand and predict the response of ecosystems to disturbance. In this study, we investigated whether there are general determinants of community response to disturbance across different community types, locations, and disturbance events. We compiled 14 case studies of community response to disturbance from four continents, twelve aquatic and terrestrial ecosystem types, and eight different types of disturbance. We used community compositional differences and species richness to indicate community response. We used mixed-effects modeling to test the relationship between each of these response metrics and four potential explanatory factors: regional species pool size, isolation, number of generations passed, and relative disturbance intensity. We found that compositional similarity was higher between pre- and post-disturbance communities when the disturbed community was connected to adjacent undisturbed habitat. The number of generations that had passed since the disturbance event was a significant, but weak, predictor of community compositional change; two communities were responsible for the observed relationship. We found no significant relationships between the factors we tested and changes in species richness. To our knowledge, this is the first attempt to search for general drivers of community resilience from a diverse set of case studies. The strength of the relationship between compositional change and isolation suggests that it may be informative in resilience research and biodiversity management

Sum rules and energy scales in the high-temperature superconductor YBa2Cu3O6+x

The Ferrell-Glover-Tinkham (FGT) sum rule has been applied to the temperature dependence of the in-plane optical conductivity of optimally-doped YBa_2Cu_3O_{6.95} and underdoped YBa_2Cu_3O_{6.60}. Within the accuracy of the experiment, the sum rule is obeyed in both materials. However, the energy scale \omega_c required to recover the full strength of the superfluid \rho_s in the two materials is dramatically different; \omega_c \simeq 800 cm^{-1} in the optimally doped system (close to twice the maximum of the superconducting gap, 2\Delta_0), but \omega_c \gtrsim 5000 cm^{-1} in the underdoped system. In both materials, the normal-state scattering rate close to the critical temperature is small, \Gamma < 2\Delta_0, so that the materials are not in the dirty limit and the relevant energy scale for \rho_s in a BCS material should be twice the energy gap. The FGT sum rule in the optimally-doped material suggests that the majority of the spectral weight of the condensate comes from energies below 2\Delta_0, which is consistent with a BCS material in which the condensate originates from a Fermi liquid normal state. In the underdoped material the larger energy scale may be a result of the non-Fermi liquid nature of the normal state. The dramatically different energy scales suggest that the nature of the normal state creates specific conditions for observing the different aspects of what is presumably a central mechanism for superconductivity in these materials.Comment: RevTeX 4 file, 9 pages with 7 embedded eps figure

Stripes, Pseudogaps, and Van Hove Nesting in the Three-band tJ Model

Slave boson calculations have been carried out in the three-band tJ model for the high-T_c cuprates, with the inclusion of coupling to oxygen breathing mode phonons. Phonon-induced Van Hove nesting leads to a phase separation between a hole-doped domain and a (magnetic) domain near half filling, with long-range Coulomb forces limiting the separation to a nanoscopic scale. Strong correlation effects pin the Fermi level close to, but not precisely at the Van Hove singularity (VHS), which can enhance the tendency to phase separation. The resulting dispersions have been calculated, both in the uniform phases and in the phase separated regime. In the latter case, distinctly different dispersions are found for large, random domains and for regular (static) striped arrays, and a hypothetical form is presented for dynamic striped arrays. The doping dependence of the latter is found to provide an excellent description of photoemission and thermodynamic experiments on pseudogap formation in underdoped cuprates. In particular, the multiplicity of observed gaps is explained as a combination of flux phase plus charge density wave (CDW) gaps along with a superconducting gap. The largest gap is associated with VHS nesting. The apparent smooth evolution of this gap with doping masks a crossover from CDW-like effects near optimal doping to magnetic effects (flux phase) near half filling. A crossover from large Fermi surface to hole pockets with increased underdoping is found. In the weakly overdoped regime, the CDW undergoes a quantum phase transition ($T_{CDW}\to 0$), which could be obscured by phase separation.Comment: 15 pages, Latex, 18 PS figures Corrects a sign error: major changes, esp. in Sect. 3, Figs 1-4,6 replace

Spin-Charge Separation in the t−Jt-J Model: Magnetic and Transport Anomalies

A real spin-charge separation scheme is found based on a saddle-point state of the $t-J$ model. In the one-dimensional (1D) case, such a saddle-point reproduces the correct asymptotic correlations at the strong-coupling fixed-point of the model. In the two-dimensional (2D) case, the transverse gauge field confining spinon and holon is shown to be gapped at {\em finite doping} so that a spin-charge deconfinement is obtained for its first time in 2D. The gap in the gauge fluctuation disappears at half-filling limit, where a long-range antiferromagnetic order is recovered at zero temperature and spinons become confined. The most interesting features of spin dynamics and transport are exhibited at finite doping where exotic {\em residual} couplings between spin and charge degrees of freedom lead to systematic anomalies with regard to a Fermi-liquid system. In spin dynamics, a commensurate antiferromagnetic fluctuation with a small, doping-dependent energy scale is found, which is characterized in momentum space by a Gaussian peak at ($\pi/a$, $\pi/a$) with a doping-dependent width ($\propto \sqrt{\delta}$, $\delta$ is the doping concentration). This commensurate magnetic fluctuation contributes a non-Korringa behavior for the NMR spin-lattice relaxation rate. There also exits a characteristic temperature scale below which a pseudogap behavior appears in the spin dynamics. Furthermore, an incommensurate magnetic fluctuation is also obtained at a {\em finite} energy regime. In transport, a strong short-range phase interference leads to an effective holon Lagrangian which can give rise to a series of interesting phenomena including linear-$T$ resistivity and $T^2$ Hall-angle. We discuss the striking similarities of these theoretical features with those found in the high-$T_c$ cuprates and give aComment: 70 pages, RevTex, hard copies of 7 figures available upon request; minor revisions in the text and references have been made; To be published in July 1 issue of Phys. Rev. B52, (1995

Structural response of Caribbean dry forests to hurricane winds: a case study from Guanica Forest, Puerto Rico

Tropical dry forests in the Caribbean have an uniquely short, shrubby structure with a high proportion of multiple-stemmed trees compared to dry forests elsewhere in the Neotropics. Previous studies have shown that this structure can arise without the loss of main stems from cutting, grazing, or other human intervention. The Caribbean has a high frequency of hurricanes, so wind may also influence forest stature. Furthermore, these forests also tend to grow on soils with low amounts of available phosphorus, which may also influence structure. The objective of this study was to assess the role of high winds in structuring dry forest, and to determine whether soil nutrient pools influence forest response following hurricane disturbance. Methods: Over 2000 stems in five plots were sampled for hurricane effects within 1 week after Hurricane Georges impacted field sites in 1998. Sprout initiation, growth, and mortality were analysed for 1407 stems for 2 years after the hurricane. Soil nutrient pools were measured at the base of 456 stems to assess association between nutrients and sprout dynamics. Results: Direct effects of the hurricane were minimal, with stem mortality at \u3c 2% and structural damage to stems at 13%, although damage was biased toward stems of larger diameter. Sprouting response was high . over 10 times as many trees had sprouts after the hurricane as before. The number of sprouts on a stem also increased significantly. Sprouting was common on stems that only suffered defoliation or had no visible effects from the hurricane. Sprout survival after 2 years was also high (\u3e 86%). Soil nutrient pools had little effect on forest response as a whole, but phosphorus supply did influence sprout dynamics on four of the more common tree species. Main Conclusions: Hurricanes are able to influence Caribbean tropical dry forest structure by reducing average stem diameter and basal area and generating significant sprouting responses. New sprouts, with ongoing survival, will maintain the high frequency of multi-stemmed trees found in this region. Sprouting is not limited to damaged stems, indicating that trees are responding to other aspects of high winds, such as short-term gravitational displacement or sway. Soil nutrients play a secondary role in sprouting dynamics of a subset of species. The short, shrubby forest structure common to the Caribbean can arise naturally as a response to hurricane winds