Algorithms to solve the Sutherland model

We give a self-contained presentation and comparison of two different algorithms to explicitly solve quantum many body models of indistinguishable particles moving on a circle and interacting with two-body potentials of $1/\sin^2$-type. The first algorithm is due to Sutherland and well-known; the second one is a limiting case of a novel algorithm to solve the elliptic generalization of the Sutherland model. These two algorithms are different in several details. We show that they are equivalent, i.e., they yield the same solution and are equally simple.Comment: 15 pages, LaTe

Explicit solution of the (quantum) elliptic Calogero-Sutherland model

We derive explicit formulas for the eigenfunctions and eigenvalues of the elliptic Calogero-Sutherland model as infinite series, to all orders and for arbitrary particle numbers and coupling parameters. The eigenfunctions obtained provide an elliptic deformation of the Jack polynomials. We prove in certain special cases that these series have a finite radius of convergence in the nome $q$ of the elliptic functions, including the two particle (= Lam\'e) case for non-integer coupling parameters.Comment: v1: 17 pages. The solution is given as series in q but only to low order. v2: 30 pages. Results significantly extended. v3: 35 pages. Paper completely revised: the results of v1 and v2 are extended to all order

Elementary Derivation of the Chiral Anomaly

An elementary derivation of the chiral gauge anomaly in all even dimensions is given in terms of noncommutative traces of pseudo-differential operators.Comment: Minor errors and misprints corrected, a reference added. AmsTex file, 12 output pages. If you do not have preloaded AmsTex you have to \input amstex.te

Volcanic ash as fertiliser for the surface ocean

Iron is a key limiting micro-nutrient for marine primary productivity. It can be supplied to the ocean by atmospheric dust deposition. Volcanic ash deposition into the ocean represents another external and so far largely neglected source of iron. This study demonstrates strong evidence for natural fertilisation in the iron-limited oceanic area of the NE Pacific, induced by volcanic ash from the eruption of Kasatochi volcano in August 2008. Atmospheric and oceanic conditions were favourable to generate a massive phytoplankton bloom in the NE Pacific Ocean which for the first time strongly suggests a connection between oceanic iron-fertilisation and volcanic ash supply

Atmospheric transport and deposition of Indonesian volcanic emissions

International audienceA regional climate model has been used to study the transport and deposition of sulfur (SO2 and SO42-) and PbCl2 emissions from Indonesian volcanoes. The sensitivity of the atmospheric loss of these trace species to meteorological conditions and their solubility was examined. Two experiments were conducted: 1) volcanic sulfur released as primarily SO2 and subject to transport, deposition, and oxidation to SO42-; and 2) PbCl2 released as an infinitely soluble passive tracer subject to only transport and deposition. The first experiment was used to calculate SO2 loss rates from each active Indonesian volcano producing an annual mean loss rate for all volcanoes of 1.1×10-5 s-1, or an e-folding rate of approximately 1 day. SO2 loss rate was found to vary seasonally, be poorly correlated with wind speed, and uncorrelated with temperature or relative humidity. The variability of SO2 loss rates is found to be correlated with the variability of wind speeds, suggesting that it is much more difficult to establish a "typical'' SO2 loss rate for volcanoes that are exposed to changeable winds. Within an average distance of 70 km away from the active Indonesian volcanoes, 53% of SO2 loss is due to conversion to SO42-, 42% due to dry deposition, and 5% due to lateral transport away from the dominant direction of plume travel. The solubility of volcanic emissions in water is shown to influence their atmospheric transport and deposition. High concentrations of PbCl2 are predicted to be deposited near to the volcanoes while volcanic S travels further away until removal from the atmosphere primarily via the wet deposition of H2SO4. The ratio of the concentration of PbCl2 to SO2 is found to exponentially decay at increasing distance from the volcanoes. The more rapid removal of highly soluble species should be considered when observing SO2 in an aged plume and relating this concentration to other volcanic species. An assumption that the ratio between the concentrations of highly soluble volcanic compounds and SO2 within a plume is equal to that observed in fumarolic gases is reasonable at small distances from the volcanic vent, but will result in an underestimation of the emission flux of highly soluble species

Induced Gauge Theory on a Noncommutative Space

We consider a scalar $\phi^4$ theory on canonically deformed Euclidean space in 4 dimensions with an additional oscillator potential. This model is known to be renormalisable. An exterior gauge field is coupled in a gauge invariant manner to the scalar field. We extract the dynamics for the gauge field from the divergent terms of the 1-loop effective action using a matrix basis and propose an action for the noncommutative gauge theory, which is a candidate for a renormalisable model.Comment: Typos corrected, one reference added; eqn. (49) corrected, one equation number added; 30 page

Generalized local interactions in 1D: solutions of quantum many-body systems describing distinguishable particles

As is well-known, there exists a four parameter family of local interactions in 1D. We interpret these parameters as coupling constants of delta-type interactions which include different kinds of momentum dependent terms, and we determine all cases leading to many-body systems of distinguishable particles which are exactly solvable by the coordinate Bethe Ansatz. We find two such families of systems, one with two independent coupling constants deforming the well-known delta interaction model to non-identical particles, and the other with a particular one-parameter combination of the delta- and (so-called) delta-prime interaction. We also find that the model of non-identical particles gives rise to a somewhat unusual solution of the Yang-Baxter relations. For the other model we write down explicit formulas for all eigenfunctions.Comment: 23 pages v2: references adde

Instantons and the Ground State of the Massive Schwinger Model

We study the massive Schwinger model, quantum electrodynamics of massive, Dirac fermions, in 1+1 dimensions; with space compactified to a circle. In the limit that transitions to fermion--anti-fermion pairs can be neglected, we study the full ground state. We focus on the effect of instantons which mediate tunnelling transitions in the induced potential for the dynamical degree of freedom in the gauge field.Comment: 17 pages, plain te

Phase diagrams of the 2D t-t'-U Hubbard model from an extended mean field method

It is well-known from unrestricted Hartree-Fock computations that the 2D Hubbard model does not have homogeneous mean field states in significant regions of parameter space away from half filling. This is incompatible with standard mean field theory. We present a simple extension of the mean field method that avoids this problem. As in standard mean field theory, we restrict Hartree-Fock theory to simple translation invariant states describing antiferromagnetism (AF), ferromagnetism (F) and paramagnetism (P), but we use an improved method to implement the doping constraint allowing us to detect when a phase separated state is energetically preferred, e.g. AF and F coexisting at the same time. We find that such mixed phases occur in significant parts of the phase diagrams, making them much richer than the ones from standard mean field theory. Our results for the 2D t-t'-U Hubbard model demonstrate the importance of band structure effects.Comment: 6 pages, 5 figure

Noncommutative Induced Gauge Theory

We consider an external gauge potential minimally coupled to a renormalisable scalar theory on 4-dimensional Moyal space and compute in position space the one-loop Yang-Mills-type effective theory generated from the integration over the scalar field. We find that the gauge invariant effective action involves, beyond the expected noncommutative version of the pure Yang-Mills action, additional terms that may be interpreted as the gauge theory counterpart of the harmonic oscillator term, which for the noncommutative $\phi^4$-theory on Moyal space ensures renormalisability. The expression of a possible candidate for a renormalisable action for a gauge theory defined on Moyal space is conjectured and discussed.Comment: 20 pages, 6 figure