Calogero-Sutherland Type Models in Higher Dimensions

We construct two different Calogero-Sutherland type models with only two-body interactions in arbitrary dimensions. We obtain some exact wave functions, including the ground states, of these two models for arbitrary number of spinless nonrelativistic particles.Comment: RevTeX, 10 pages, few minor changes, version to appear in Physics Letters

Maternal Cardiovascular Impairment in Pregnancies Complicated by Severe Fetal Growth Restriction

Abstract—Fetal growth restriction and preeclampsia are both conditions of placental etiology and associated to increased risk for the long-term development of cardiovascular disease in the mother. At presentation, preeclampsia is associated with maternal global diastolic dysfunction, which is determined, at least in part, by increased afterload and myocardial stiffness. The aim of this study is to test the hypothesis that women with normotensive fetal growth-restricted pregnancies also exhibit global diastolic dysfunction. This was a prospective case-control study conducted over a 3-year period involving 29 preterm fetal growth-restricted pregnancies, 25 preeclamptic with fetal growth restriction pregnancies, and 58 matched control pregnancies. Women were assessed by conventional echocardiography and tissue Doppler imaging at diagnosis of the complication and followed-up at 12 weeks postpartum. Fetal growth-restricted pregnancies are characterized by a lower cardiac index and higher total vascular resistance index than expected for gestation. Compared with controls, fetal growth-restricted pregnancy was associated with significantly increased prevalence (P�0.001) of asymptomatic left ventricular diastolic dysfunction (28% versus 4%) and widespread impaired myocardial relaxation (59% versus 21%). Unlike preeclampsia, cardiac geometry and intrinsic myocardial contractility were preserved in fetal growth-restricted pregnancy. Fetal growth-restricted pregnancies are characterized by a low output, high resistance circulatory state, as well as a higher prevalence of asymptomatic global diastolic dysfunction and poor cardiac reserve. These findings may explain the increased long-term cardiovascular risk in these women who have had fetal growth-restricted pregnancies. Further studies are needed to clarify the postnatal natural history of cardiac dysfunction in these women

The Numerical Simulation of Radiative Shocks I: The elimination of numerical shock instabilities using a localized oscillation filter

We address a numerical instability that arises in the directionally split computation of hydrodynamic flows when shock fronts are parallel to a grid plane. Transverse oscillations in pressure, density and temperature are produced that are exacerbated by thermal instability when cooling is present, forming post--shock `stripes'. These are orthogonal to the classic post--shock 'ringing' fluctuations. The resulting post--shock `striping' substantially modifies the flow. We discuss three different methods to resolve this problem. These include (1) a method based on artificial viscosity; (2) grid--jittering and (3) a new localized oscillation filter that acts on specific grid cells in the shock front. These methods are tested using a radiative wall shock problem with an embedded shear layer. The artificial viscosity method is unsatisfactory since, while it does reduce post--shock ringing, it does not eliminate the stripes and the excessive shock broadening renders the calculation of cooling inaccurate, resulting in an incorrect shock location. Grid--jittering effectively counteracts striping. However, elsewhere on the grid, the shear layer is unphysically diffused and this is highlighted in an extreme case. The oscillation filter method removes stripes and permits other high velocity gradient regions of the flow to evolve in a physically acceptable manner. It also has the advantage of only acting on a small fraction of the cells in a two or three dimensional simulation and does not significantly impair performance.Comment: 20 pages, 6 figures, revised version submitted to ApJ Supplement Serie

A Mean Field Analysis of One Dimensional Quantum Liquid with Long Range Interaction

Bi-local mean field theory is applied to one dimensional quantum liquid with long range $1/r^2$ interaction, which has exact ground state wave function. We obtain a mean field solution and an effective action which expresses a long range dynamics. Based on them the ground state energy and correlation functions are computed. The ground state energy agrees fairly well with the exact value and exponents have weaker coupling constant dependence than that of partly known exact value.Comment: EPHOU-93-002, 10 pages (LaTeX), 3 figures available upon request as hard cop

Exact spin-orbital separation in a solvable model in one dimension

A one-dimensional model of coupled spin-1/2 spins and pseudospin-1/2 orbitals with nearest-neighbor interaction is rigorously shown to exhibit spin-orbital separation by means of a non-local unitary transformation. On an open chain, this transformation completely decouples the spins from the orbitals in such a way that the spins become paramagnetic while the orbitals form the soluble XXZ Heisenberg model. The nature of various correlations is discussed. The more general cases, which allow spin-orbital separation by the same method, are pointed out. A generalization for the orbital pseudospin greater than 1/2 is also discussed. Some qualitative connections are drawn with the recently observed spin-orbital separation in Sr2CuO3.Comment: 5 page

Crossover from Fermi Liquid to Non-Fermi Liquid Behavior in a Solvable One-Dimensional Model

We consider a quantum moany-body problem in one-dimension described by a Jastrow type, characterized by an exponent $\lambda$ and a parameter $\gamma$. We show that with increasing $\gamma$, the Fermi Liquid state ($\gamma=0)$ crosses over to non-Fermi liquid states, characterized by effective "temperature".Comment: 8pp. late

Dyson's Brownian Motion and Universal Dynamics of Quantum Systems

We establish a correspondence between the evolution of the distribution of eigenvalues of a $N\times N$ matrix subject to a random Gaussian perturbing matrix, and a Fokker-Planck equation postulated by Dyson. Within this model, we prove the equivalence conjectured by Altshuler et al between the space-time correlations of the Sutherland-Calogero-Moser system in the thermodynamic limit and a set of two-variable correlations for disordered quantum systems calculated by them. Multiple variable correlation functions are, however, shown to be inequivalent for the two cases.Comment: 10 pages, revte

Connection between Calogero-Marchioro-Wolfes type few-body models and free oscillators

We establish the exact correspondence of the Calogero-Marchioro-Wolfes model and several of its generalizations with free oscillators. This connection yields the eigenstates and leads to a proof of the quantum integrability. The usefulness of our method for finding new solvable models is then demonstrated by an example.Comment: 10 pages, REVTeX, Minor correction

An equivalence relation of boundary/initial conditions, and the infinite limit properties

The 'n-equivalences' of boundary conditions of lattice models are introduced and it is derived that the models with n-equivalent boundary conditions result in the identical free energy. It is shown that the free energy of the six-vertex model is classified through the density of left/down arrows on the boundary. The free energy becomes identical to that obtained by Lieb and Sutherland with the periodic boundary condition, if the density of the arrows is equal to 1/2. The relation to the structure of the transfer matrix and a relation to stochastic processes are noted.Comment: 6 pages with a figure, no change but the omitted figure is adde