Isolated Eigenvalues of the Ferromagnetic Spin-J XXZ Chain with Kink Boundary Conditions

We investigate the low-lying excited states of the spin J ferromagnetic XXZ chain with Ising anisotropy Delta and kink boundary conditions. Since the third component of the total magnetization, M, is conserved, it is meaningful to study the spectrum for each fixed value of M. We prove that for J>= 3/2 the lowest excited eigenvalues are separated by a gap from the rest of the spectrum, uniformly in the length of the chain. In the thermodynamic limit, this means that there are a positive number of excitations above the ground state and below the essential spectrum

Spatially heterogeneous dynamics investigated via a time-dependent four-point density correlation function

Relaxation in supercooled liquids above their glass transition and below the onset temperature of “slow” dynamics involves the correlated motion of neighboring particles. This correlated motion results in the appearance of spatially heterogeneous dynamics or “dynamical heterogeneity.” Traditional two-point time-dependent density correlation functions, while providing information about the transient “caging” of particles on cooling, are unable to provide sufficiently detailed information about correlated motion and dynamical heterogeneity. Here, we study a four-point, time-dependent density correlation function g4(r,t)g4(r,t) and corresponding “structure factor” S4(q,t)S4(q,t) which measure the spatial correlations between the local liquid density at two points in space, each at two different times, and so are sensitive to dynamical heterogeneity. We study g4(r,t)g4(r,t) and S4(q,t)S4(q,t) via molecular dynamics simulations of a binary Lennard-Jones mixture approaching the mode coupling temperature from above. We find that the correlations between particles measured by g4(r,t)g4(r,t) and S4(q,t)S4(q,t) become increasingly pronounced on cooling. The corresponding dynamical correlation length ξ4(t)ξ4(t) extracted from the small-qq behavior of S4(q,t)S4(q,t) provides an estimate of the range of correlated particle motion. We find that ξ4(t)ξ4(t) has a maximum as a function of time t,t, and that the value of the maximum of ξ4(t)ξ4(t) increases steadily from less than one particle diameter to a value exceeding nine particle diameters in the temperature range approaching the mode coupling temperature from above. At the maximum, ξ4(t)ξ4(t) and the α relaxation time τατα are related by a power law. We also examine the individual contributions to g4(r,t),g4(r,t), S4(q,t),S4(q,t), and ξ4(t),ξ4(t), as well as the corresponding order parameter Q(t)Q(t) and generalized susceptibility χ4(t),χ4(t), arising from the self and distinct contributions to Q(t).Q(t). These contributions elucidate key differences between domains of localized and delocalized particles.© 2003 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70264/2/JCPSA6-119-14-7372-1.pd

Ferromagnetic Ordering of Energy Levels for Uq(sl2)U_q(\mathfrak{sl}_2) Symmetric Spin Chains

We consider the class of quantum spin chains with arbitrary $U_q(\mathfrak{sl}_2)$-invariant nearest neighbor interactions, sometimes called $\textrm{SU}_q(2)$ for the quantum deformation of $\textrm{SU}(2)$, for $q>0$. We derive sufficient conditions for the Hamiltonian to satisfy the property we call {\em Ferromagnetic Ordering of Energy Levels}. This is the property that the ground state energy restricted to a fixed total spin subspace is a decreasing function of the total spin. Using the Perron-Frobenius theorem, we show sufficient conditions are positivity of all interactions in the dual canonical basis of Lusztig. We characterize the cone of positive interactions, showing that it is a simplicial cone consisting of all non-positive linear combinations of "cascade operators," a special new basis of $U_q(\mathfrak{sl}_2)$ intertwiners we define. We also state applications to interacting particle processes.Comment: 23 page

β-Alanine Supplementation Has No Effect on Rowing Performance in College Age Athletes

Please view abstract in the attached PDF file

Estimated pre-morbid IQ effects on cognitive and functional outcomes in Alzheimer disease: a longitudinal study in a treated cohort

Abstract Background Cognitive reserve is thought to influence the degree of neuropathology needed for diagnosis of Alzheimer disease (AD). Cognitive reserve can be operationally defined as the hypothesized capacity of the mature adult brain to sustain the effects of disease or injury without manifesting clinical symptoms of AD, but sufficient to cause clinical dementia in an individual possessing less cognitive reserve. Its effect on the subsequent course of AD is less clear. Pre-morbid IQ is a useful measure of cognitive reserve. Methods We studied 659 consecutive patients with AD at a tertiary referral memory clinic. Patients were assessed on six cognitive tests at baseline. Activities of Daily Living (ADL) were measured on the Instrumental Activities of Daily Living (IADL) scale and Physical Self-Maintenance Scale (PSMS). The National Adult Reading Test (NART) was used to estimate pre-morbid IQ. Patients were followed up after starting a cholinesterase inhibitor over 78 weeks. Mixed general linear models estimated the effects of NART on cognition and ADL. Results Three hundred and fifty-five patients had NART scored with a mean estimated pre-morbid IQ of 104.7 (standard deviation 18.5). NART increased overall cognitive ability by 2.7% for every 10 IQ points (p Conclusion Our data support the hypothesis that cognitive reserve continues to have a limited influence on cognition after AD has been diagnosed and thus, indirectly, has an impact on ADL.</p

Interface Roughening in a Hydrodynamic Lattice-Gas Model with Surfactant

Using a hydrodynamic lattice-gas model, we study interface growth in a binary fluid with various concentrations of surfactant. We find that the interface is smoothed by small concentrations of surfactant, while microemulsion droplets form for large surfactant concentrations. To assist in determining the stability limits of the interface, we calculate the change in the roughness and growth exponents $\alpha$ and $\beta$ as a function of surfactant concentration along the interface.Comment: 4 pages with 4 embedded ps figures. Requires psfig.tex. Will appear in PRL 14 Oct 199

Thermodynamic and structural aspects of the potential energy surface of simulated water

Relations between the thermodynamics and dynamics of supercooled liquids approaching a glass transition have been proposed over many years. The potential energy surface of model liquids has been increasingly studied since it provides a connection between the configurational component of the partition function on one hand, and the system dynamics on the other. This connection is most obvious at low temperatures, where the motion of the system can be partitioned into vibrations within a basin of attraction and infrequent inter-basin transitions. In this work, we present a description of the potential energy surface properties of supercooled liquid water. The dynamics of this model has been studied in great details in the last years. Specifically, we locate the minima sampled by the liquid by ``quenches'' from equilibrium configurations generated via molecular dynamics simulations. We calculate the temperature and density dependence of the basin energy, degeneracy, and shape. The temperature dependence of the energy of the minima is qualitatively similar to simple liquids, but has anomalous density dependence. The unusual density dependence is also reflected in the configurational entropy, the thermodynamic measure of degeneracy. Finally, we study the structure of simulated water at the minima, which provides insight on the progressive tetrahedral ordering of the liquid on cooling