Eigenvalue estimates for the Aharonov-Bohm operator in a domain

We prove semi-classical estimates on moments of eigenvalues of the Aharonov-Bohm operator in bounded two-dimensional domains. Moreover, we present a counterexample to the generalized diamagnetic inequality which was proposed by Erdos, Loss and Vougalter. Numerical studies complement these results.Comment: 22 pages, 10 figure

Dynamical two electron states in a Hubbard-Davydov model

We study a model in which a Hubbard Hamiltonian is coupled to the dispersive phonons in a classical nonlinear lattice. Our calculations are restricted to the case where we have only two quasi-particles of opposite spins, and we investigate the dynamics when the second quasi-particle is added to a state corresponding to a minimal energy single quasi-particle state. Depending on the parameter values, we find a number of interesting regimes. In many of these, discrete breathers (DBs) play a prominent role with a localized lattice mode coupled to the quasiparticles. Simulations with a purely harmonic lattice show much weaker localization effects. Our results support the possibility that DBs are important in HTSC.Comment: 14 pages, 12 fig

Explicit Solution to the N-Body Calogero Problem

We solve the N-body Calogero problem, \ie N particles in 1 dimension subject to a two-body interaction of the form \half \sum_{i,j}[ (x_i - x_j)^2 + g/ {(x_i - x_j)^2}], by constructing annihilation and creation operators of the form $a_i^\mp =\frac 1 {\sqrt 2} (x _i \pm i\hat{p}_i )$, where $\hat{p}_i$ is a modified momentum operator obeying %!!!!!!! Heisenberg-type commutation relations with $x_i$, involving explicitly permutation operators. On the other hand, $D_j =i\,\hat{p}_j$ can be interpreted as a covariant derivative corresponding to a flat connection. The relation to fractional statistics in 1+1 dimensions and anyons in a strong magnetic field is briefly discussed.Comment: 6 p., latex, USITP-92-

A Generalization of the Brodsky-Lepage Formalism

We present an approach that generalizes in a natural way the perturbative QCD formalism developed by Brodsky and Lepage for the study of exclusive hadronic processes to the case of $L\neq 0$ mesons. As an application of our approach we consider here the production of meson pairs, involving tensor and pseudotensor mesons, in photon-photon collisions.Comment: LaTeX, 5 pages, 1 embedded ps figure, uses macros sprocl.sty, epsfig.sty. Talk delivered by F. Murgia at the PHOTON'97 Conference, Egmond aan Zee, The Netherlands, May 10-15, 1997. To be published in the proceedings by World Scientifi

A new scale to assess the therapeutic relationship in community mental health care: STAR

Background. No instrument has been developed specifically for assessing the clinician-patient therapeutic relationship (TR) in community psychiatry. This study aimed to develop a measure of the TR with clinician and patient versions using psychometric principles for test construction. Method. A four-stage prospective study was undertaken, comprising qualitative semi-structured interviews about TRs with clinicians and patients and their assessment of nine established scales for their applicability to community care, administering an amalgamated scale of more than 100 items, followed by Principal Components Analysis (PCA) of these ratings for preliminary scale construction. test-retest reliability of the scale and administering the scale in a new sample to confirm its factorial structure. The sample consisted of patients with severe mental illness and a designated key worker in the care of 17 community mental health teams in England and Sweden. Results. New items not covered by established scales were identified, including clinician helpfulness in accessing services, patient aggression and family interference. The new patient (STAR-P) and clinician scales (STAR-C) each have 12 items comprising three subscales: positive collaboration and positive clinician input in both versions, non-supportive clinician input in the patient version, and emotional difficulties in the clinician version. Test-retest reliability was r = 0(.)76 for STAR-P and r = 0(.)68 for STAR-C. The factorial structure of the new scale was confirmed with a good fit. Conclusions. STAR is a specifically developed, brief scale to assess TRs in community psychiatry with good psychometric properties and is suitable for use in research and routine care

Friends and Symptom Dimensions in Patients with Psychosis: A Pooled Analysis

PMCID: PMC3503760This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited

Quadratic cavity soliton optical frequency combs

We theoretically investigate the formation of frequency combs in a dispersive second-harmonic generation cavity system, and predict the existence of quadratic cavity solitons in the absence of a temporal walk-off

Press perturbation experiments and the indeterminacy of ecological interactions: effects of taxonomic resolution and experimental duration

The outcomes of press perturbation experiments on community dynamics are difficult to predict because there is a high degree of indeterminacy in the strength and direction of ecological interactions. Ecologists need to quantify uncertainties in estimates of interaction strength, by determining all the possible values a given interaction strength could take and the relative likelihood of each value. In this study, we assess the degree to which fish effects on zooplankton and phytoplankton are indeterminate in direction using a combination of experimental data and Monte Carlo simulations. Based on probability distributions of interaction strength (i.e. effect magnitude), we estimated the probability of each fish interaction being negative, positive or undetermined in direction. We then investigated how interaction strength and its predictability might vary with experimental duration and the taxonomic resolution of food web data. Results show that most effects of fish on phyto- and zooplankton were indeed indeterminate, and that the effects of fish were more predictable in direction as the taxonomic resolution of food web data decreased and the experimental duration increased. Results also show that most distributions of interaction strength were not normal, suggesting that normal based statistical procedures for testing hypothesis about interaction strength may be misleading, as well as predictions of food web models assuming normal distributions of interaction strength. By considering the probability distributions and confidence intervals of interaction parameters, ecologists would better understand the outcomes of species interactions and make more realistic predictions about our perturbations in natural food webs