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

International scientific research on venture capital: a bibliometric and mapping analysis from the period 1978–2020

The aim of this study is to explore the relevance of scientific production on venture capital using bibliometric and mapping tools.We performed a search in Scopus, involving any document published between 1978 and 2020. We used bibliometric indicators to explore documents production, dispersion, distribution, time of duplication, and annual growth, as Price’s law of scientific literature growth, Lotka’s law, the transient index, and the Bradford model. We also calculated the participation index of the different countries and institutions. Finally, we explored the co-occurrence and thematic networks for the most frequently used terms in venture capital research through bibliometric mapping.A total of 1,230 original articles were collected from the timeframe 1978–2020. The model confirms that Price’s law is not fulfilled. Scientific production was better adjusted to linear growth (r = 0.9290) than exponential (r = 0.9161). Literature on venture capital research has increased its growth in the last 43 years at a rate of 7.9% per year, with a production that doubles its size every 9.1 years. The transience index was 79.91%, which indicates that most of the scientific production is due to a lot of authors with a small number of publications on the research topic. Bradford´s law shows that the scientific production in this area is widely distributed in multiple journals, and Lotka’s law indicates that the author’s distribution is heavily concentrated on small producers. The United States of America (USA) and the University of Pennsylvania present the highest production, contributing 31.22% and 1.63% of the total production of research on venture capital.The venture capital task has undergone a linear growth, with a very high rate of transience, which indicates the presence of numerous authors who sporadically publish on this topic. No evidence of a saturation point was observed in the scientific production analyzed, which makes it possible to conclude that the research in venture capital will continue to be in demand by the scientific community.The aim of this study is to explore the relevance of scientific production on venture capital using bibliometric and mapping tools.We performed a search in Scopus, involving any document published between 1978 and 2020. We used bibliometric indicators to explore documents production, dispersion, distribution, time of duplication, and annual growth, as Price’s law of scientific literature growth, Lotka’s law, the transient index, and the Bradford model. We also calculated the participation index of the different countries and institutions. Finally, we explored the co-occurrence and thematic networks for the most frequently used terms in venture capital research through bibliometric mapping.A total of 1,230 original articles were collected from the timeframe 1978–2020. The model confirms that Price’s law is not fulfilled. Scientific production was better adjusted to linear growth (r = 0.9290) than exponential (r = 0.9161). Literature on venture capital research has increased its growth in the last 43 years at a rate of 7.9% per year, with a production that doubles its size every 9.1 years. The transience index was 79.91%, which indicates that most of the scientific production is due to a lot of authors with a small number of publications on the research topic. Bradford´s law shows that the scientific production in this area is widely distributed in multiple journals, and Lotka’s law indicates that the author’s distribution is heavily concentrated on small producers. The United States of America (USA) and the University of Pennsylvania present the highest production, contributing 31.22% and 1.63% of the total production of research on venture capital.The venture capital task has undergone a linear growth, with a very high rate of transience, which indicates the presence of numerous authors who sporadically publish on this topic. No evidence of a saturation point was observed in the scientific production analyzed, which makes it possible to conclude that the research in venture capital will continue to be in demand by the scientific community