Exact Solution of a One-Dimensional Multicomponent Lattice Gas with Hyperbolic Interaction

We present the exact solution to a one-dimensional multicomponent quantum lattice model interacting by an exchange operator which falls off as the inverse-sinh-square of the distance. This interaction contains a variable range as a parameter, and can thus interpolate between the known solutions for the nearest-neighbor chain, and the inverse-square chain. The energy, susceptibility, charge stiffness and the dispersion relations for low-lying excitations are explicitly calculated for the absolute ground state, as a function of both the range of the interaction and the number of species of fermions.Comment: 13 REVTeX pages + 5 uuencoded figures, UoU-003059

Solution of Some Integrable One-Dimensional Quantum Systems

In this paper, we investigate a family of one-dimensional multi-component quantum many-body systems. The interaction is an exchange interaction based on the familiar family of integrable systems which includes the inverse square potential. We show these systems to be integrable, and exploit this integrability to completely determine the spectrum including degeneracy, and thus the thermodynamics. The periodic inverse square case is worked out explicitly. Next, we show that in the limit of strong interaction the "spin" degrees of freedom decouple. Taking this limit for our example, we obtain a complete solution to a lattice system introduced recently by Shastry, and Haldane; our solution reproduces the numerical results. Finally, we emphasize the simple explanation for the high multiplicities found in this model

Spectral flow in the supersymmetric tt-JJ model with a 1/r21/r^2 interaction

The spectral flow in the supersymmetric {\it t-J} model with $1/r^2$ interaction is studied by analyzing the exact spectrum with twisted boundary conditions. The spectral flows for the charge and spin sectors are shown to nicely fit in with the motif picture in the asymptotic Bethe ansatz. Although fractional exclusion statistics for the spin sector clearly shows up in the period of the spectral flow at half filling, such a property is generally hidden once any number of holes are doped, because the commensurability condition in the motif is not met in the metallic phase.Comment: 8 pages, revtex, Phys. Rev. B54 (1996) August 15, in pres

Partially Solvable Anisotropic t-J Model with Long-Range Interactions

A new anisotropic t-J model in one dimension is proposed which has long-range hopping and exchange. This t-J model is only partially solvable in contrast to known integrable models with long-range interaction. In the high-density limit the model reduces to the XXZ chain with the long-range exchange. Some exact eigenfunctions are shown to be of Jastrow-type if certain conditions for an anisotropy parameter are satisfied. The ground state as well as the excitation spectrum for various cases of the anisotropy parameter and filling are derived numerically. It is found that the Jastrow-type wave function is an excellent trial function for any value of the anisotropy parameter.Comment: 10 pages, 3 Postscript figure

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

Exact Solution of Heisenberg-liquid models with long-range coupling

We present the exact solution of two Heisenberg-liquid models of particles with arbitrary spin $S$ interacting via a hyperbolic long-range potential. In one model the spin-spin coupling has the simple antiferromagnetic Heisenberg exchange form, while for the other model the interaction is of the ferromagnetic Babujian-Takhatajan type. It is found that the Bethe ansatz equations of these models have a similar structure to that of the Babujian-Takhatajan spin chain. We also conjecture the integrability of a third new spin-lattice model with long-range interaction.Comment: 7pages Revte

Supersymmetry, Shape Invariance and Solvability of AN−1A_{N-1} and BCNBC_{N} Calogero-Sutherland Model

Using the ideas of supersymmetry and shape invariance we re-derive the spectrum of the $A_{N-1}$ and $BC_N$ Calogero-Sutherland model. We briefly discuss as to how to obtain the corresponding eigenfunctions. We also discuss the difficulties involved in extending this approach to the trigonometric models.Comment: 15 pages, REVTeX,No figure

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

Solutions to the Multi-Component 1/R Hubbard Model

In this work we introduce one dimensional multi-component Hubbard model of 1/r hopping and U on-site energy. The wavefunctions, the spectrum and the thermodynamics are studied for this model in the strong interaction limit $U=\infty$. In this limit, the system is a special example of $SU(N)$ Luttinger liquids, exhibiting spin-charge separation in the full Hilbert space. Speculations on the physical properties of the model at finite on-site energy are also discussed.Comment: 9 pages, revtex, Princeton-May1

Correlations in an expanding gas of hard-core bosons

We consider a longitudinal expansion of a one-dimensional gas of hard-core bosons suddenly released from a trap. We show that the broken translational invariance in the initial state of the system is encoded in correlations between the bosonic occupation numbers in the momentum space. The correlations are protected by the integrability and exhibit no relaxation during the expansion