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

Conservation laws in the continuum 1/r21/r^2 systems

We study the conservation laws of both the classical and the quantum mechanical continuum $1/r^2$ type systems. For the classical case, we introduce new integrals of motion along the recent ideas of Shastry and Sutherland (SS), supplementing the usual integrals of motion constructed much earlier by Moser. We show by explicit construction that one set of integrals can be related algebraically to the other. The difference of these two sets of integrals then gives rise to yet another complete set of integrals of motion. For the quantum case, we first need to resum the integrals proposed by Calogero, Marchioro and Ragnisco. We give a diagrammatic construction scheme for these new integrals, which are the quantum analogues of the classical traces. Again we show that there is a relationship between these new integrals and the quantum integrals of SS by explicit construction.Comment: 19 RevTeX 3.0 pages with 2 PS-figures include

Patterns of Late Cenozoic exhumation deduced from apatite and zircon U-He ages from Fiordland, New Zealand

New apatite and zircon (U-Th)/He ages from the Fiordland region of New Zealand's South Island expand on earlier results and provide new constraints on patterns of Late Cenozoic exhumation and cooling across this region. Zircon (U-Th)/He cooling ages, in combination with increased density of apatite ages, show that in addition to a gradual northward decrease in cooling ages that was seen during an earlier phase of this study, there is also a trend toward younger cooling ages to the east. Distinct breaks in cooling age patterns on southwestern Fiordland appear to be correlated to the location of previously mapped faults. The northward decrease in ages may reflect asynchronous cooling related to migration in the locus of exhumation driven by subduction initiation, or it may reflect synchronous regional exhumation that exposed different structural levels across Fiordland, or some combination of these effects. In either case, differential exhumation accommodated by major and minor faults that dissect Fiordland basement rocks apparently played an important role in producing the resulting age patterns

Solution of Some Integrable One-Dimensional Quantum Systems

In this paper, we investigate a family of one-dimensional multi-component quantum many-body systems. The interaction is an exchange interaction based on the familiar family of integrable systems which includes the inverse square potential. We show these systems to be integrable, and exploit this integrability to completely determine the spectrum including degeneracy, and thus the thermodynamics. The periodic inverse square case is worked out explicitly. Next, we show that in the limit of strong interaction the "spin" degrees of freedom decouple. Taking this limit for our example, we obtain a complete solution to a lattice system introduced recently by Shastry, and Haldane; our solution reproduces the numerical results. Finally, we emphasize the simple explanation for the high multiplicities found in this model

Eisenstein Series and String Thresholds

We investigate the relevance of Eisenstein series for representing certain $G(Z)$-invariant string theory amplitudes which receive corrections from BPS states only. $G(Z)$ may stand for any of the mapping class, T-duality and U-duality groups $Sl(d,Z)$, $SO(d,d,Z)$ or $E_{d+1(d+1)}(Z)$ respectively. Using $G(Z)$-invariant mass formulae, we construct invariant modular functions on the symmetric space $K\backslash G(R)$ of non-compact type, with $K$ the maximal compact subgroup of $G(R)$, that generalize the standard non-holomorphic Eisenstein series arising in harmonic analysis on the fundamental domain of the Poincar\'e upper half-plane. Comparing the asymptotics and eigenvalues of the Eisenstein series under second order differential operators with quantities arising in one- and $g$-loop string amplitudes, we obtain a manifestly T-duality invariant representation of the latter, conjecture their non-perturbative U-duality invariant extension, and analyze the resulting non-perturbative effects. This includes the $R^4$ and $R^4 H^{4g-4}$ couplings in toroidal compactifications of M-theory to any dimension $D\geq 4$ and $D\geq 6$ respectively.Comment: Latex2e, 60 pages; v2: Appendix A.4 extended, 2 refs added, thms renumbered, plus minor corrections; v3: relation (1.7) to math Eis series clarified, eq (3.3) and minor typos corrected, final version to appear in Comm. Math. Phys; v4: misprints and Eq C.13,C.24 corrected, see note adde

On a Matrix Model of Level Structure

We generalize the dimensionally reduced Yang-Mills matrix model by adding d=1 Chern-Simons term and terms for a bosonic vector. The coefficient, \kappa of the Chern-Simons term must be integer, and hence the level structure. We show at the bottom of the Yang-Mills potential, the low energy limit, only the linear motion is allowed for D0 particles. Namely all the particles align themselves on a single straight line subject to \kappa^2/r^2 repulsive potential from each other. We argue the relevant brane configuration to be D0-branes in a D4 after \kappa of D8's pass the system.Comment: 1+6 pages, No figure, LaTeX; Minor changes; To appear in Class. Quant. Gra

Exact Solution of Heisenberg-liquid models with long-range coupling

We present the exact solution of two Heisenberg-liquid models of particles with arbitrary spin $S$ interacting via a hyperbolic long-range potential. In one model the spin-spin coupling has the simple antiferromagnetic Heisenberg exchange form, while for the other model the interaction is of the ferromagnetic Babujian-Takhatajan type. It is found that the Bethe ansatz equations of these models have a similar structure to that of the Babujian-Takhatajan spin chain. We also conjecture the integrability of a third new spin-lattice model with long-range interaction.Comment: 7pages Revte

High time resolution observation of the transient event of 5 March 1979

The detection of an intense gamma ray burst with the monitor proportional counter on the HEAO 2 spacecraft is discussed with particular emphasis on the measurement of the time of onset of the event. Based on the mean observed counting rate in the burst and assuming a sharp rise, the uncertainty in the burst onset is found to be + or - 220 microseconds. The time of occurrence was 57124.826908 + or - 0.000220 s UT on March 5, 1979, and the location of the HEAO 2 satellite at this time was latitude 22.15 deg, longitude -27.60 deg at an altitude of 525.0 km