A class of Calogero type reductions of free motion on a simple Lie group

The reductions of the free geodesic motion on a non-compact simple Lie group G based on the $G_+ \times G_+$ symmetry given by left- and right multiplications for a maximal compact subgroup $G_+ \subset G$ are investigated. At generic values of the momentum map this leads to (new) spin Calogero type models. At some special values the `spin' degrees of freedom are absent and we obtain the standard $BC_n$ Sutherland model with three independent coupling constants from SU(n+1,n) and from SU(n,n). This generalization of the Olshanetsky-Perelomov derivation of the $BC_n$ model with two independent coupling constants from the geodesics on $G/G_+$ with G=SU(n+1,n) relies on fixing the right-handed momentum to a non-zero character of $G_+$. The reductions considered permit further generalizations and work at the quantized level, too, for non-compact as well as for compact G.Comment: shortened to 13 pages in v2 on request of Lett. Math. Phys. and corrected some spelling error

New spin Calogero-Sutherland models related to B_N-type Dunkl operators

We construct several new families of exactly and quasi-exactly solvable BC_N-type Calogero-Sutherland models with internal degrees of freedom. Our approach is based on the introduction of two new families of Dunkl operators of B_N type which, together with the original B_N-type Dunkl operators, are shown to preserve certain polynomial subspaces of finite dimension. We prove that a wide class of quadratic combinations involving these three sets of Dunkl operators always yields a spin Calogero-Sutherland model, which is (quasi-)exactly solvable by construction. We show that all the spin Calogero-Sutherland models obtainable within this framework can be expressed in a unified way in terms of a Weierstrass P function with suitable half-periods. This provides a natural spin counterpart of the well-known general formula for a scalar completely integrable potential of BC_N type due to Olshanetsky and Perelomov. As an illustration of our method, we exactly compute several energy levels and their corresponding wavefunctions of an elliptic quasi-exactly solvable potential for two and three particles of spin 1/2.Comment: 18 pages, typeset in LaTeX 2e using revtex 4.0b5 and the amslatex package Minor changes in content, one reference adde

Inozemtsev's hyperbolic spin model and its related spin chain

In this paper we study Inozemtsev's su(m) quantum spin model with hyperbolic interactions and the associated spin chain of Haldane-Shastry type introduced by Frahm and Inozemtsev. We compute the spectrum of Inozemtsev's model, and use this result and the freezing trick to derive a simple analytic expression for the partition function of the Frahm-Inozemtsev chain. We show that the energy levels of the latter chain can be written in terms of the usual motifs for the Haldane-Shastry chain, although with a different dispersion relation. The formula for the partition function is used to analyze the behavior of the level density and the distribution of spacings between consecutive unfolded levels. We discuss the relevance of our results in connection with two well-known conjectures in quantum chaos.Comment: 22 pages, RevTeX, 7 figure

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

Inflaton Fragmentation and Oscillon Formation in Three Dimensions

Analytical arguments suggest that a large class of scalar field potentials permit the existence of oscillons -- pseudo-stable, non-topological solitons -- in three spatial dimensions. In this paper we numerically explore oscillon solutions in three dimensions. We confirm the existence of these field configurations as solutions to the Klein-Gorden equation in an expanding background, and verify the predictions of Amin and Shirokoff for the characteristics of individual oscillons for their model. Further, we demonstrate that significant numbers of oscillons can be generated via fragmentation of the inflaton condensate, consistent with the analysis of Amin. These emergent oscillons can easily dominate the post-inflationary universe. Finally, both analytic and numerical results suggest that oscillons are stable on timescales longer than the post-inflationary Hubble time. Consequently, the post-inflationary universe can contain an effective matter-dominated phase, during which it is dominated by localized concentrations of scalar field matter.Comment: See http://easther.physics.yale.edu/downloads.html for numerical codes. Visualizations available at http://www.mit.edu/~mamin/oscillons.html and http://easther.physics.yale.edu/fields.html V2 Minor fixes to reference lis

Generalized Zeta Functions and One-loop Corrections to Quantum Kink Masses

A method for describing the quantum kink states in the semi-classical limit of several (1+1)-dimensional field theoretical models is developed. We use the generalized zeta function regularization method to compute the one-loop quantum correction to the masses of the kink in the sine-Gordon and cubic sinh-Gordon models and another two ${\rm P}(\phi)_2$ systems with polynomial self-interactions.Comment: 29 pages, 4 figures; version to appear in Nucl. Phys.

An exactly solvable supersymmetric spin chain of BC_N type

We construct a new exactly solvable supersymmetric spin chain related to the BC_N extended root system, which includes as a particular case the BC_N version of the Polychronakos-Frahm spin chain. We also introduce a supersymmetric spin dynamical model of Calogero type which yields the new chain in the large coupling limit. This connection is exploited to derive two different closed-form expressions for the chain's partition function by means of Polychronakos's freezing trick. We establish a boson-fermion duality relation for the new chain's spectrum, which is in fact valid for a large class of (not necessarily integrable) spin chains of BC_N type. The exact expressions for the partition function are also used to study the chain's spectrum as a whole, showing that the level density is normally distributed even for a moderately large number of particles. We also determine a simple analytic approximation to the distribution of normalized spacings between consecutive levels which fits the numerical data with remarkable accuracy. Our results provide further evidence that spin chains of Haldane-Shastry type are exceptional integrable models, in the sense that their spacings distribution is not Poissonian, as posited by the Berry-Tabor conjecture for "generic'' quantum integrable systems.Comment: 36 pages, 7 figure

A beryllium-10 chronology of late-glacial moraines in the upper Rakaia valley, Southern Alps, New Zealand supports Southern- Hemisphere warming during the Younger Dryas

Interhemispheric differences in the timing of pauses or reversals in the temperature rise at the end of the last ice age can help to clarify the mechanisms that influence glacial terminations. Our beryllium-10 (10Be) surface-exposure chronology for the moraines of the upper Rakaia valley of New Zealand's Southern Alps, combined with glaciological modeling, show that late-glacial temperature change in the atmosphere over the Southern Alps exhibited an Antarctic-like pattern. During the Antarctic Cold Reversal, the upper Rakaia glacier built two well-defined, closely-spaced moraines on Reischek knob at 13,900 ± 120 [1σ; ± 310 yrs when including a 2.1% production-rate (PR) uncertainty] and 13,140 ± 250 (±370) yrs ago, in positions consistent with mean annual temperature approximately 2 °C cooler than modern values. The formation of distinct, widely-spaced moraines at 12,140 ± 200 (±320) and 11,620 ± 160 (±290) yrs ago on Meins Knob, 2 km up-valley from the Reischek knob moraines, indicates that the glacier thinned by ∼250 m during Heinrich Stadial 0 (HS 0, coeval with the Younger Dryas 12,900 to 11,600 yrs ago). The glacier-inferred temperature rise in the upper Rakaia valley during HS 0 was about 1 °C. Because a similar pattern is documented by well-dated glacial geomorphologic records from the Andes of South America, the implication is that this late-glacial atmospheric climate signal extended from 79°S north to at least 36°S, and thus was a major feature of Southern Hemisphere paleoclimate during the last glacial termination

Chapter 4 Design Options, Implementation Issues and Evaluating Success of Ecologically Engineered Shorelines

Human population growth and accelerating coastal development have been the drivers for unprecedented construction of artificial structures along shorelines globally. Construction has been recently amplified by societal responses to reduce flood and erosion risks from rising sea levels and more extreme storms resulting from climate change. Such structures, leading to highly modified shorelines, deliver societal benefits, but they also create significant socioeconomic and environmental challenges. The planning, design and deployment of these coastal structures should aim to provide multiple goals through the application of ecoengineering to shoreline development. Such developments should be designed and built with the overarching objective of reducing negative impacts on nature, using hard, soft and hybrid ecological engineering approaches. The design of ecologically sensitive shorelines should be context-dependent and combine engineering, environmental and socioeconomic considerations. The costs and benefits of ecoengineered shoreline design options should be considered across all three of these disciplinary domains when setting objectives, informing plans for their subsequent maintenance and management and ultimately monitoring and evaluating their success. To date, successful ecoengineered shoreline projects have engaged with multiple stakeholders (e.g. architects, engineers, ecologists, coastal/port managers and the general public) during their conception and construction, but few have evaluated engineering, ecological and socioeconomic outcomes in a comprehensive manner. Increasing global awareness of climate change impacts (increased frequency or magnitude of extreme weather events and sea level rise), coupled with future predictions for coastal development (due to population growth leading to urban development and renewal, land reclamation and establishment of renewable energy infrastructure in the sea) will increase the demand for adaptive techniques to protect coastlines. In this review, we present an overview of current ecoengineered shoreline design options, the drivers and constraints that influence implementation and factors to consider when evaluating the success of such ecologically engineered shorelines