A DMRG Study of Low-Energy Excitations and Low-Temperature Properties of Alternating Spin Systems

We use the density matrix renormalization group (DMRG) method to study the ground and low-lying excited states of three kinds of uniform and dimerized alternating spin chains. The DMRG procedure is also employed to obtain low-temperature thermodynamic properties of these systems. We consider a 2N site system with spins $s_1$ and $s_2$ alternating from site to site and interacting via a Heisenberg antiferromagnetic exchange. The three systems studied correspond to $(s_1 ,s_2 )$ being equal to $(1,1/2),(3/2,1/2)$ and $(3/2,1)$; all of them have very similar properties. The ground state is found to be ferrimagnetic with total spin $s_G =N(s_1 - s_2)$. We find that there is a gapless excitation to a state with spin $s_G -1$, and a gapped excitation to a state with spin $s_G +1$. Surprisingly, the correlation length in the ground state is found to be very small for this gapless system. The DMRG analysis shows that the chain is susceptible to a conditional spin-Peierls instability. Furthermore, our studies of the magnetization, magnetic susceptibility $\chi$ and specific heat show strong magnetic-field dependences. The product $\chi T$ shows a minimum as a function of temperature T at low magnetic fields; the minimum vanishes at high magnetic fields. This low-field behavior is in agreement with earlier experimental observations. The specific heat shows a maximum as a function of temperature, and the height of the maximum increases sharply at high magnetic fields. Although all the three systems show qualitatively similar behavior, there are some notable quantitative differences between the systems in which the site spin difference, $|s_1 - s_2|$, is large and small respectively.Comment: 16 LaTeX pages, 13 postscript figure

Non-Gaussian Radio-Wave Scattering in the Interstellar Medium

It was recently suggested by Boldyrev & Gwinn that the characteristics of radio scintillations from distant pulsars are best understood if the interstellar electron-density fluctuations that cause the time broadening of the radio pulses obey non-Gaussian statistics. In this picture the density fluctuations are inferred to be strong on very small scales ($\sim 10^8-10^{10} {cm}$). We argue that such density structures could correspond to the ionized boundaries of molecular regions (clouds) and demonstrate that the power-law distribution of scattering angles that is required to match the observations arises naturally from the expected intersections of our line of sight with randomly distributed, thin, approximately spherical ionized shells of this type. We show that the observed change in the time-broadening behavior for pulsar dispersion measures $\lesssim 30 {\rm pc} {\rm cm}^{-3}$ is consistent with the expected effect of the general ISM turbulence, which should dominate the scattering for nearby pulsars. We also point out that if the clouds are ionized by nearby stars, then their boundaries may become turbulent on account of an ionization front instability. This turbulence could be an alternative cause of the inferred density structures. An additional effect that might contribute to the strength of the small-scale fluctuations in this case is the expected flattening of the turbulent density spectrum when the eddy sizes approach the proton gyroscale.Comment: 15 pages, 3 figures, accepted to Ap

Exchange Interactions and High-Energy Spin States in Mn_12-acetate

We perform inelastic neutron scattering measurements on the molecular nanomagnet Mn_12-acetate to measure the excitation spectrum up to 45meV (500K). We isolate magnetic excitations in two groups at 5-6.5meV (60-75K) and 8-10.5meV (95-120K), with higher levels appearing only at 27meV (310K) and 31meV (360K). From a detailed characterization of the transition peaks we show that all of the low-energy modes appear to be separate S = 9 excitations above the S = 10 ground state, with the peak at 27meV (310K) corresponding to the first S = 11 excitation. We consider a general model for the four exchange interaction parameters of the molecule. The static susceptibility is computed by high-temperature series expansion and the energy spectrum, matrix elements and ground-state spin configuration by exact diagonalization. The theoretical results are matched with experimental observation by inclusion of cluster anisotropy parameters, revealing strong constraints on possible parameter sets. We conclude that only a model with dominant exchange couplings J_1 ~ J_2 ~ 5.5meV (65K) and small couplings J_3 ~ J_4 ~ 0.6meV (7K) is consistent with the experimental data.Comment: 17 pages, 12 figure

Anomalous Radio-Wave Scattering from Interstellar Plasma Structures

This paper considers scattering screens that have arbitrary spatial variations of scattering strength transverse to the line of sight, including screens that are spatially well confined, such as disks and filaments. We calculate the scattered image of a point source and the observed pulse shape of a scattered impulse. The consequences of screen confinement include: (1) Source image shapes that are determined by the physical extent of the screen rather than by the shapes of much-smaller diffracting microirregularities. These include image elongations and orientations that are frequency dependent. (2) Variation with frequency of angular broadening that is much weaker than the trademark \nu^{-2} scaling law (for a cold, unmagnetized plasma), including frequency-independent cases; and (3) Similar departure of the pulse broadening time from the usually expected \nu^{-4} scaling law. We briefly discuss applications that include scattering of pulses from the Crab pulsar by filaments in the Crab Nebula; image asymmetries from Galactic scattering of the sources Cyg X-3, Sgr A*, and NGC 6334B; and scattering of background active galactic nuclei by intervening galaxies. We also address the consequences for inferences about the shape of the wavenumber spectrum of electron density irregularities, which depend on scaling laws for the image size and the pulse broadening. Future low-frequency (< 100 MHz) array observations will also be strongly affected by the Galactic structure of scattering material. Our formalism is derived in the context of radio scattering by plasma density fluctuations. It is also applicable to optical, UV and X-ray scattering by grains in the interstellar medium.Comment: 21 pages, LaTeX2e with AASTeX-4.0, 6 PostScript figures, accepted by ApJ, revised version has minor changes to respond to referee comments and suggestion

Scoring and psychometric validation of the Perception of Anticoagulant Treatment Questionnaire (PACT-Q©)

<p>Abstract</p> <p>Background</p> <p>The 'Perception of Anti-Coagulant Treatment Questionnaire' (PACT-Q) was developed to assess patients' expectations of, and satisfaction with their anticoagulant treatment. This questionnaire needs to be finalised and psychometrically validated.</p> <p>Methods</p> <p>The PACT-Q was included in the United States, the Netherlands and France into three phase III multinational clinical trials conducted to evaluate efficacy and safety of a new long-acting anticoagulant drug (idraparinux) compared to vitamin K antagonist (VKA). PACT-Q was administered to patients with deep venous thrombosis (DVT), atrial fibrillation (AF) or pulmonary embolism (PE) at Day 1, to assess patients' expectations, and at 3 and 6 months to assess patients' satisfaction and treatment convenience and burden. The final structure of the PACT-Q (Principal Component Analysis – PCA – with Varimax Rotation) was first determined and its psychometric properties were then measured with validity of the structure (Multitrait analysis), internal consistency reliability (Cronbach's alpha coefficients) and known-group validity.</p> <p>Results</p> <p>PCA and multitrait analyses showed the multidimensionality of the "Treatment Expectations" dimension, comprising 7 items that had to be scored independently. The "Convenience" and "Burden of Disease and Treatment" dimensions of the hypothesised original structure of the questionnaire were combined, thus resulting in 13 items grouped into the single dimension "Convenience". The "Anticoagulant Treatment Satisfaction" dimension remained unchanged and included 7 items. All items of the "Convenience" and "Anticoagulant Treatment Satisfaction" dimensions displayed good convergent and discriminant validity. The internal consistency reliability was good, with a Cronbach's alpha of 0.84 for the "Convenience" dimension, and 0.76 for the "Anticoagulant Treatment Satisfaction" dimension. Known-group validity was good, especially with regard to occurrence of thromboembolic events within 3 months from randomisation.</p> <p>Conclusion</p> <p>The PACT-Q is a valid and reliable instrument that allows the assessment of patients' expectations and satisfaction regarding anticoagulant treatment, as well as their opinion about treatment convenience of use. Its two-part structure – assessment of expectations at baseline in the first part, and of convenience, burden and treatment satisfaction in the second – was validated and displays good and stable psychometric properties. These results are not sufficient to recommend the use of satisfaction as primary endpoint in clinical trials; further validation work is needed to support the interpretation of PACT-Q dimension scores. However, this first validation makes the PACT-Q an appropriate measure for use in clinical and pharmacoepidemiological research, as well as in real-life studies.</p> <p>Trial Registration</p> <p>(ClinicalTrials.gov numbers, NCT00067093, NCT00062803 and NCT00070655).</p

Nonlinear spin relaxation in strongly nonequilibrium magnets

A general theory is developed for describing the nonlinear relaxation of spin systems from a strongly nonequilibrium initial state, when, in addition, the sample is coupled to a resonator. Such processes are characterized by nonlinear stochastic differential equations. This makes these strongly nonequilibrium processes principally different from the spin relaxation close to an equilibrium state, which is represented by linear differential equations. The consideration is based on a realistic microscopic Hamiltonian including the Zeeman terms, dipole interactions, exchange interactions, and a single-site anisotropy. The influence of cross correlations between several spin species is investigated. The critically important function of coupling between the spin system and a resonant electric circuit is emphasized. The role of all main relaxation rates is analyzed. The phenomenon of self-organization of transition coherence in spin motion, from the quantum chaotic stage of incoherent fluctuations, is thoroughly described. Local spin fluctuations are found to be the triggering cause for starting the spin relaxation from an incoherent nonequilibrium state. The basic regimes of collective coherent spin relaxation are studied.Comment: Latex file, 31 page

Renormalized Effective Actions in Radially Symmetric Backgrounds I: Partial Wave Cutoff Method

The computation of the one-loop effective action in a radially symmetric background can be reduced to a sum over partial-wave contributions, each of which is the logarithm of an appropriate one-dimensional radial determinant. While these individual radial determinants can be evaluated simply and efficiently using the Gel'fand-Yaglom method, the sum over all partial-wave contributions diverges. A renormalization procedure is needed to unambiguously define the finite renormalized effective action. Here we use a combination of the Schwinger proper-time method, and a resummed uniform DeWitt expansion. This provides a more elegant technique for extracting the large partial-wave contribution, compared to the higher order radial WKB approach which had been used in previous work. We illustrate the general method with a complete analysis of the scalar one-loop effective action in a class of radially separable SU(2) Yang-Mills background fields. We also show that this method can be applied to the case where the background gauge fields have asymptotic limits appropriate to uniform field strengths, such as for example in the Minkowski solution, which describes an instanton immersed in a constant background. Detailed numerical results will be presented in a sequel.Comment: 35 page

Teachers of Latino students reflect on the implementation of a mathematical task

Teachers in two multi-grade study groups in elementary schools with large populations of Latino students reflect on the implementation of an open-ended mathematical task. IN this research, interviews and study group discussions provide the teachers’ reflections on the implementation of the task and on their practices in general that create learning environments for their Latino students. Multiple categories representing the teacher reflections were developed and our focus is on those practices that teachers consider effective and specific factors that impact practice. The design of this study proved to be especially useful in promoting teacher reflective conversation

One-Center Charge Transfer Transitions in Manganites

In frames of a rather conventional cluster approach, which combines the crystal field and the ligand field models we have considered different charge transfer (CT) states and O 2p-Mn 3d CT transitions in MnO$_{6}^{9-}$ octahedra. The many-electron dipole transition matrix elements were calculated using the Racah algebra for the cubic point group. Simple "local" approximation allowed to calculate the relative intensity for all dipole-allowed $\pi -\pi$ and $\sigma -\sigma$ CT transitions. We present a self-consistent description of the CT bands in insulating stoichiometric LaMn$^{3+}$O$_3$ compound with the only Mn$^{3+}$ valent state and idealized octahedral MnO$_{6}^{9-}$ centers which allows to substantially correct the current interpretation of the optical spectra. Our analysis shows the multi-band structure of the CT optical response with the weak low-energy edge at 1.7 eV, associated with forbidden $t_{1g}(\pi)-e_{g}$ transition and a series of the weak and strong dipole-allowed high-energy transitions starting from 2.5 and 4.5 eV, respectively, and extending up to nearly 11 eV. The most intensive features are associated with two strong composite bands near $4.6\div 4.7$ eV and $8\div 9$ eV, respectively, resulting from the superposition of the dipole-allowed $\sigma -\sigma$ and $\pi -\pi$ CT transitions. These predictions are in good agreement with experimental spectra. The experimental data point to a strong overscreening of the crystal field parameter $Dq$ in the CT states of MnO$_{6}^{9-}$ centers.Comment: 10 pages, 3 figure

Trees with Given Stability Number and Minimum Number of Stable Sets

We study the structure of trees minimizing their number of stable sets for given order $n$ and stability number $\alpha$. Our main result is that the edges of a non-trivial extremal tree can be partitioned into $n-\alpha$ stars, each of size $\lceil \frac{n-1}{n-\alpha} \rceil$ or $\lfloor \frac{n-1}{n-\alpha}\rfloor$, so that every vertex is included in at most two distinct stars, and the centers of these stars form a stable set of the tree.Comment: v2: Referees' comments incorporate