Quasi-Exactly Solvable N-Body Spin Hamiltonians with Short-Range Interaction Potentials

We review some recent results on quasi-exactly solvable spin models presenting near-neighbors interactions. These systems can be understood as cyclic generalizations of the usual Calogero-Sutherland models. A nontrivial modification of the exchange operator formalism is used to obtain several infinite families of eigenfunctions of these models in closed form.Comment: This is a contribution to the Proc. of workshop on Geometric Aspects of Integrable Systems (July 17-19, 2006; Coimbra, Portugal), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

A Haldane-Shastry spin chain of BC_N type in a constant magnetic field

We compute the spectrum of the trigonometric Sutherland spin model of BC_N type in the presence of a constant magnetic field. Using Polychronakos's freezing trick, we derive an exact formula for the partition function of its associated Haldane-Shastry spin chain.Comment: LaTeX, 13 page

The Berry-Tabor conjecture for spin chains of Haldane-Shastry type

According to a long-standing conjecture of Berry and Tabor, the distribution of the spacings between consecutive levels of a "generic'' integrable model should follow Poisson's law. In contrast, the spacings distribution of chaotic systems typically follows Wigner's law. An important exception to the Berry-Tabor conjecture is the integrable spin chain with long-range interactions introduced by Haldane and Shastry in 1988, whose spacings distribution is neither Poissonian nor of Wigner's type. In this letter we argue that the cumulative spacings distribution of this chain should follow the "square root of a logarithm'' law recently proposed by us as a characteristic feature of all spin chains of Haldane-Shastry type. We also show in detail that the latter law is valid for the rational counterpart of the Haldane-Shastry chain introduced by Polychronakos.Comment: LaTeX with revtex4, 6 pages, 6 figure

The Radio Jet Associated with the Multiple V380 Ori System

The giant Herbig-Haro object 222 extends over $\sim$6$'$ in the plane of the sky, with a bow shock morphology. The identification of its exciting source has remained uncertain over the years. A non-thermal radio source located at the core of the shock structure was proposed to be the exciting source. However, Very Large Array studies showed that the radio source has a clear morphology of radio galaxy and a lack of flux variations or proper motions, favoring an extragalactic origin. Recently, an optical-IR study proposed that this giant HH object is driven by the multiple stellar system V380 Ori, located about 23$'$ to the SE of HH 222. The exciting sources of HH systems are usually detected as weak free-free emitters at centimeter wavelengths. Here we report the detection of an elongated radio source associated with the Herbig Be star or with its close infrared companion in the multiple V380 Ori system. This radio source has the characteristics of a thermal radio jet and is aligned with the direction of the giant outflow defined by HH~222 and its suggested counterpart to the SE, HH~1041. We propose that this radio jet traces the origin of the large scale HH outflow. Assuming that the jet arises from the Herbig Be star, the radio luminosity is a few times smaller than the value expected from the radio-bolometric correlation for radio jets, confirming that this is a more evolved object than those used to establish the correlation.Comment: 13 pages, 3 figure

Moving embedded lattice solitons

It was recently proved that isolated unstable "embedded lattice solitons" (ELS) may exist in discrete systems. The discovery of these ELS gives rise to relevant questions such as the following: are there continuous families of ELS?, can ELS be stable?, is it possible for ELS to move along the lattice?, how do ELS interact?. The present work addresses these questions by showing that a novel differential-difference equation (a discrete version of a complex mKdV equation) has a two-parameter continuous family of exact ELS. The numerical tests reveal that these solitons are stable and robust enough to withstand collisions. The model may apply to the description of a Bose-Einstein condensate with dipole-dipole interactions between the atoms, trapped in a deep optical-lattice potential.Comment: 13 pages, 11 figure