Black hole solutions in 2+1 dimensions

We give circularly symmetric solutions for null fluid collapse in 2+1-dimensional Einstein gravity with a cosmological constant. The fluid pressure $P$ and energy density $\rho$ are related by $P=k\rho$ $(k\le 1)$. The long time limit of the solutions are black holes whose horizon structures depend on the value of $k$. The $k=1$ solution is the Banados-Teitelboim-Zanelli black hole metric in the long time static limit, while the $k<1$ solutions give other, `hairy' black hole metrics in this limit.Comment: 8 pages, RevTeX (to appear in Phys. Rev. D) References to Mann and Ross, and Mann, Chan and Chan adde

Superparamagnetic-like ac susceptibility behavior in a "partially disordered antiferromagnetic" compound, Ca3_3CoRhO6_6

We report the results of dc and ac magnetization measurements as a function of temperature (1.8 - 300 K) for the spin chain compound, Ca$_3$CoRhO$_6$, which has been recently reported to exhibit a partially disordered antiferromagnetic (PDAF) structure in the range 30 - 90 K and spin-glass freezing below 30 K. We observe an unexpectedly large frequency dependence of ac susceptibility in the T range 30 - 90 K, typical of superparamagnets. In addition, we find that there is no difference in the isothermal remanent magnetization behavior for the two regimes below 90 K. These findings call for more investigations to understand the magnetism of this compound.Comment: 4 pages, 3 figure

Proportion Regulation in Globally Coupled Nonlinear Systems

As a model of proportion regulation in differentiation process of biological system, globally coupled activator-inhibitor systems are studied. Formation and destabilization of one and two cluster state are predicted analytically. Numerical simulations show that the proportion of units of clusters is chosen within a finite range and it is selected depend on the initial condition.Comment: 11 pages (revtex format) and 5 figures (PostScript)

S=1/2 chains and spin-Peierls transition in TiOCl

We study TiOCl as an example of an S=1/2 layered Mott insulator. From our analysis of new susceptibility data, combined with LDA and LDA+U band structure calculations, we conclude that orbital ordering produces quasi-one-dimensional spin chains and that TiOCl is a new example of Heisenberg-chains which undergo a spin-Peierls transition. The energy scale is an order of magnitude larger than that of previously known examples. The effects of non-magnetic Sc impurities are explained using a model of broken finite chains.Comment: 5 pages, 5 figures (color); details on crystal growth added; to be published in Phys. Rev.

Global Nonradial Instabilities of Dynamically Collapsing Gas Spheres

Self-similar solutions provide good descriptions for the gravitational collapse of spherical clouds or stars when the gas obeys a polytropic equation of state, $p=K\rho^\gamma$ (with $\gamma\le 4/3$). We study the behaviors of nonradial perturbations in the similarity solutions of Larson, Penston and Yahil, which describe the evolution of the collapsing cloud prior to core formation. Our global stability analysis reveals the existence of unstable bar-modes ($l=2$) when $\gamma\le 1.09$. In particular, for the collapse of isothermal spheres, which applies to the early stages of star formation, the $l=2$ density perturbation relative to the background, $\delta\rho({\bf r},t)/\rho(r,t)$, increases as $(t_0-t)^{-0.352}\propto \rho_c(t)^{0.176}$, where $t_0$ denotes the epoch of core formation, and $\rho_c(t)$ is the cloud central density. Thus, the isothermal cloud tends to evolve into an ellipsoidal shape (prolate bar or oblate disk, depending on initial conditions) as the collapse proceeds. In the context of Type II supernovae, core collapse is described by the $\gamma\simeq 1.3$ equation of state, and our analysis indicates that there is no growing mode (with density perturbation) in the collapsing core before the proto-neutron star forms, although nonradial perturbations can grow during the subsequent accretion of the outer core and envelope onto the neutron star. We also carry out a global stability analysis for the self-similar expansion-wave solution found by Shu, which describes the post-collapse accretion (``inside-out'' collapse) of isothermal gas onto a protostar. We show that this solution is unstable to perturbations of all $l$'s, although the growth rates are unknown.Comment: 28 pages including 7 ps figures; Minor changes in the discussion; To be published in ApJ (V.540, Sept.10, 2000 issue

Comment on piNN Coupling from High Precision np Charge Exchange at 162 MeV

In this updated and expanded version of our delayed Comment we show that the np backward cross section, as presented by the Uppsala group, is seriously flawed (more than 25 sd.). The main reason is the incorrect normalization of the data. We show also that their extrapolation method, used to determine the charged piNN coupling constant, is a factor of about 10 less accurate than claimed by Ericson et al. The large extrapolation error makes the determination of the coupling constant by the Uppsala group totally uninteresting.Comment: 5 pages, latex2e with a4wide.sty. This is an updated and extended version of the Comment published in Phys. Rev. Letters 81, 5253 (1998

Extraction of the πNN\pi NN coupling constant from NN scattering data

We reexamine Chew's method for extracting the $\pi NN$ coupling constant from np differential cross section measurements. Values for this coupling are extracted below 350 MeV, in the potential model region, and up to 1 GeV. The analyses to 1~GeV have utilized 55 data sets. We compare these results to those obtained via $\chi^2$ mapping techniques. We find that these two methods give consistent results which are in agreement with previous Nijmegen determinations.Comment: 12 pages of text plus 2 figures. Revtex file and postscript figures available via anonymous FTP at ftp://clsaid.phys.vt.edu/pub/n

Natural Thermal and Magnetic Entanglement in 1D Heisenberg Model

We investigate the entanglement between any two spins in a one dimensional Heisenberg chain as a function of temperature and the external magnetic field. We find that the entanglement in an antiferromagnetic chain can be increased by increasing the temperature or the external field. Increasing the field can also create entanglement between otherwise disentangled spins. This entanglement can be confirmed by testing Bell's inequalities involving any two spins in the solid.Comment: 4 pages, 5 figure

Spin-Peierls and Antiferromagnetic Phases in Cu{1-x}Zn{x}GeO{3}: A Neutron Scattering Study

Comprehensive neutron scattering studies were carried out on a series of high-quality single crystals of Cu_{1-x}Zn_xGeO_3. The Zn concentration, x, was determined for each sample using Electron Probe Micro-Analysis. The measured Zn concentrations were found to be 40-80% lower than the nominal values. Nevertheless the measured concentrations cover a wide range which enables a systematic study of the effects due to Zn-doping. We have confirmed the coexistence of spin-Peierls (SP) and antiferromagnetic (AF) orderings at low temperatures and the measured phase diagram is presented. Most surprisingly, long-range AF ordering occurs even in the lowest available Zn concentration, x=0.42%, which places important constraints on theoretical models of the AF-SP coexistence. Magnetic excitations are also examined in detail. The AF excitations are sharp at low energies and show no considerable broadening as x increases indicating that the AF ordering remains long ranged for x up to 4.7%. On the other hand, the SP phase exhibits increasing disorder as x increases, as shown from the broadening of the SP excitations as well as the dimer reflection peaks.Comment: 17 preprint style pages, 9 postscript files included. Submitted to Phys. Rev. B. Also available from http://insti.physics.sunysb.edu/~mmartin/pubs.htm

Entangled Rings

Consider a ring of N qubits in a translationally invariant quantum state. We ask to what extent each pair of nearest neighbors can be entangled. Under certain assumptions about the form of the state, we find a formula for the maximum possible nearest-neighbor entanglement. We then compare this maximum with the entanglement achieved by the ground state of an antiferromagnetic ring consisting of an even number of spin-1/2 particles. We find that, though the antiferromagnetic ground state does not maximize the nearest-neighbor entanglement relative to all other states, it does so relative to other states having zero z-component of spin.Comment: 19 pages, no figures; v2 includes new results; v3 corrects a numerical error for the case N=