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

High Resolution Imaging of the Magnetic Field in the central parsec of the Galaxy

We discuss a high resolution (FWHM~ 0.45 arcsec) image of the emissive polarization from warm dust in the minispiral in the Galactic Centre and discuss the implications for the magnetic field in the dusty filaments. The image was obtained at a wavelength of 12.5 microns with the CanariCam multimode mid-infrared imager on the Gran Telescopio Canarias. It confirms the results obtained from previous observations but also reveals new details of the polarization structures. In particular, we identify regions of coherent magnetic field emission at position angles of ~45 deg to the predominantly north--south run of field lines in the Northern Arm which may be related to orbital motions inclined to the general flow of the Northern Arm. The luminous stars that have been identified as bow-shock sources in the Northern Arm do not disrupt or dilute the field but are linked by a coherent field structure, implying that the winds from these objects may push and compress the field but do not overwhelm it. The magnetic field in the the low surface brightness regions in the East-West Bar to the south of SgrA* lies along the Bar, but the brighter regions generally have different polarization position angles, suggesting that they are distinct structures. In the region of the Northern Arm sampled here, there is only a weak correlation between the intensity of the emission and the degree of polarization. This is consistent with saturated grain alignment where the degree of polarization depends on geometric effects, including the angle of inclination of the field to the line of sight and superposition of filaments with different field directions, rather than the alignment efficiency.Comment: 9 pages, 3 figures, Proceedings of Cosmic Dust X, held in Mitaka, Japan in August 201

Kinematics of the Outflow From The Young Star DG Tau B: Rotation in the vicinities of an optical jet

We present $^{12}$CO(2-1) line and 1300 $\mu$m continuum observations made with the Submillimeter Array (SMA) of the young star DG Tau B. We find, in the continuum observations, emission arising from the circumstellar disk surrounding DG Tau B. The $^{12}$CO(2-1) line observations, on the other hand, revealed emission associated with the disk and the asymmetric outflow related with this source. Velocity asymmetries about the flow axis are found over the entire length of the flow. The amplitude of the velocity differences is of the order of 1 -- 2 km s$^{-1}$ over distances of about 300 -- 400 AU. We interpret them as a result of outflow rotation. The sense of the outflow and disk rotation is the same. Infalling gas from a rotating molecular core cannot explain the observed velocity gradient within the flow. Magneto-centrifugal disk winds or photoevaporated disk winds can produce the observed rotational speeds if they are ejected from a keplerian disk at radii of several tens of AU. Nevertheless, these slow winds ejected from large radii are not very massive, and cannot account for the observed linear momentum and angular momentum rates of the molecular flow. Thus, the observed flow is probably entrained material from the parent cloud. DG Tau B is a good laboratory to model in detail the entrainment process and see if it can account for the observed angular momentum.Comment: Accepted to Ap