GAPS IN THE HEISENBERG-ISING MODEL

We report on the closing of gaps in the ground state of the critical Heisenberg-Ising chain at momentum $\pi$. For half-filling, the gap closes at special values of the anisotropy $\Delta= \cos(\pi/Q)$, $Q$ integer. We explain this behavior with the help of the Bethe Ansatz and show that the gap scales as a power of the system size with variable exponent depending on $\Delta$. We use a finite-size analysis to calculate this exponent in the critical region, supplemented by perturbation theory at $\Delta\sim 0$. For rational $1/r$ fillings, the gap is shown to be closed for {\em all} values of $\Delta$ and the corresponding perturbation expansion in $\Delta$ shows a remarkable cancellation of various diagrams.Comment: 12 RevTeX pages + 4 figures upon reques

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

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

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

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

Universal Level dynamics of Complex Systems

. We study the evolution of the distribution of eigenvalues of a $N\times N$ matrix subject to a random perturbation drawn from (i) a generalized Gaussian ensemble (ii) a non-Gaussian ensemble with a measure variable under the change of basis. It turns out that, in the case (i), a redefinition of the parameter governing the evolution leads to a Fokker-Planck equation similar to the one obtained when the perturbation is taken from a standard Gaussian ensemble (with invariant measure). This equivalence can therefore help us to obtain the correlations for various physically-significant cases modeled by generalized Gaussian ensembles by using the already known correlations for standard Gaussian ensembles. For large $N$-values, our results for both cases (i) and (ii) are similar to those obtained for Wigner-Dyson gas as well as for the perturbation taken from a standard Gaussian ensemble. This seems to suggest the independence of evolution, in thermodynamic limit, from the nature of perturbation involved as well as the initial conditions and therefore universality of dynamics of the eigenvalues of complex systems.Comment: 11 Pages, Latex Fil

Transport Properties of a One-Dimensional Two-Component Quantum Liquid with Hyperbolic Interactions

We present an investigation of the sinh-cosh (SC) interaction model with twisted boundary conditions. We argue that, when unlike particles repel, the SC model may be usefully viewed as a Heisenberg-Ising fluid with moving Heisenberg-Ising spins. We derive the Luttinger liquid relation for the stiffness and the susceptibility, both from conformal arguments, and directly from the integral equations. Finally, we investigate the opening and closing of the ground state gaps for both SC and Heisenberg-Ising models, as the interaction strength is varied.Comment: 10 REVTeX pages + 4 uuencoded figures, UoU-002029

The Recurrent Nature of Central Starbursts

New hydrodynamic models with feedback show that feedback driven turbulence and subsequent relaxation can drive recurrent starbursts, though most of these bursts fizzle due to premature, asymmetric ignition. Strong bursts are terminated when the turbulence inflates the multiphase central disk. The period between bursts is about twice a free-fall time onto the central disk. Transient spirals and bars are common through the burst cycle.Comment: 7 pages + 3 figs. Conf. paper for "Starbursts: from 30 Doradus to Lyman Break Galaxies," held at Inst. of Astronomy, Cambridge Univ., Sept. 6-10, 2004. Kluwer Academic Publishers, eds. R. de Grijs and R. M. Gonzalez Delgado + additional materia

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

Long Range Interaction Models and Yangian Symmetry

The generalized Sutherland-Romer models and Yan models with internal spin degrees are formulated in terms of the Polychronakos' approach and RTT relation associated to the Yang-Baxter equation in consistent way. The Yangian symmetry is shown to generate both models. We finally introduce the reflection algebra K(u) to the long range models.Comment: 13 pages, preprint of Nankai Institute of Mathematics ( Theoretical Physics Division ), published in Physical Review E of 1995. For hard copy, write to Prof. Mo-lin GE directly. Do not send emails to this accoun