On the Lagrangian Realization of the WZNW Reductions

We develop a phase space path-integral approach for deriving the Lagrangian realization of the models defined by Hamiltonian reduction of the WZNW theory. We illustrate the uses of the approach by applying it to the models of non-Abelian chiral bosons, $W$-algebras and the GKO coset construction, and show that the well-known Sonnenschein's action, the generalized Toda action and the gauged WZNW model are precisely the Lagrangian realizations of those models, respectively.Comment: 15 pages, DIAS-STP-92-09/UdeM-LPN-TH-92-9

Global description of action-angle duality for a Poisson-Lie deformation of the trigonometric BCn\mathrm{BC}_n Sutherland system

Integrable many-body systems of Ruijsenaars--Schneider--van Diejen type displaying action-angle duality are derived by Hamiltonian reduction of the Heisenberg double of the Poisson-Lie group $\mathrm{SU}(2n)$. New global models of the reduced phase space are described, revealing non-trivial features of the two systems in duality with one another. For example, after establishing that the symplectic vector space $\mathbb{C}^n\simeq\mathbb{R}^{2n}$ underlies both global models, it is seen that for both systems the action variables generate the standard torus action on $\mathbb{C}^n$, and the fixed point of this action corresponds to the unique equilibrium positions of the pertinent systems. The systems in duality are found to be non-degenerate in the sense that the functional dimension of the Poisson algebra of their conserved quantities is equal to half the dimension of the phase space. The dual of the deformed Sutherland system is shown to be a limiting case of a van Diejen system.Comment: 39 pages, some stylistic changes and typos removed in v

Global Aspects of the WZNW Reduction to Toda Theories

It is well-known that the Toda Theories can be obtained by reduction from the Wess-Zumino-Novikov-Witten (WZNW) model, but it is less known that this WZNW $\rightarrow$ Toda reduction is \lq incomplete'. The reason for this incompleteness being that the Gauss decomposition used to define the Toda fields from the WZNW field is valid locally but not globally over the WZNW group manifold, which implies that actually the reduced system is not just the Toda theory but has much richer structures. In this note we furnish a framework which allows us to study the reduced system globally, and thereby present some preliminary results on the global aspects. For simplicity, we analyze primarily 0 $+$ 1 dimensional toy models for $G = SL(n, {\bf R})$, but we also discuss the 1 $+$ 1 dimensional model for $G = SL(2, {\bf R})$ which corresponds to the WZNW $\rightarrow$ Liouville reduction.Comment: 22 pages, INS-Rep.-104

Interplay between mesoscopic phase separation and bulk magnetism in the layered NaxCoO2

Specific heat of the layered NaxCoO2 (x=0.65, 0.70 and 0.75) oxides has been measured in the temperature range of 3-360 K and magnetic field of 0 and 9 T. The analysis of data, assuming the combined effect of inter-layer superexchange and the phase separation into mesoscopic magnetic domains with localized spins embedded in a matrix with itinerant electronic character, suggests that the dominant contribution to the specific heat in the region of short-range ordering is mediated by quasi-2D antiferromagnetic clusters, perpendicular to the CoO2 layers

Trigonometric real form of the spin RS model of Krichever and Zabrodin

We investigate the trigonometric real form of the spin Ruijsenaars-Schneider system introduced, at the level of equations of motion, by Krichever and Zabrodin in 1995. This pioneering work and all earlier studies of the Hamiltonian interpretation of the system were performed in complex holomorphic settings; understanding the real forms is a non-trivial problem. We explain that the trigonometric real form emerges from Hamiltonian reduction of an obviously integrable 'free' system carried by a spin extension of the Heisenberg double of the ${\rm U}(n)$ Poisson-Lie group. The Poisson structure on the unreduced real phase space ${\rm GL}(n,\mathbb{C}) \times \mathbb{C}^{nd}$ is the direct product of that of the Heisenberg double and $d\geq 2$ copies of a ${\rm U}(n)$ covariant Poisson structure on $\mathbb{C}^n \simeq \mathbb{R}^{2n}$ found by Zakrzewski, also in 1995. We reduce by fixing a group valued moment map to a multiple of the identity, and analyze the resulting reduced system in detail. In particular, we derive on the reduced phase space the Hamiltonian structure of the trigonometric spin Ruijsenaars-Schneider system and we prove its degenerate integrability.Comment: 52 pages, 1 figure. v2: typos removed, final versio

Poisson Structures of Calogero-Moser and Ruijsenaars-Schneider Models

We examine the Hamiltonian structures of some Calogero-Moser and Ruijsenaars-Schneider N-body integrable models. We propose explicit formulations of the bihamiltonian structures for the discrete models, and field-theoretical realizations of these structures. We discuss the relevance of these realizations as collective-field theory for the discrete models.Comment: 15 pages, no figures; v2 references added, typos correcte

System Approaches for the Analysis of Water Quality Management of the Sio, Kapos, Veszpremi-Sed, Malom, Nador, and Gaja River System (Hungary)

The current challenge for water quality management in Central Europe and Eastern Europe is to identify feasible and cost-effective strategies for achieving sustainable progress towards improved water quality. This goal is set against a background of existing water quality standards which are strong but difficult to enforce, the changing role of the public sector after the fall of central planning, limited financial resources and the uncertainty and weak economic conditions of the transition. Within this context, successful water quality management requires strategies that are: (a) administratively enforceable; (b) strengthen and stabilize water quality management institutions; (c) financially feasible; (d) promote economic efficiency; and (e) fairly distribute costs over responsible parties. The Sio, Kapos, Veszpremi-Sed, Malom, Nador and Gaja River System epitomizes this need and confronts nearly all of the serious water management problems now facing Hungary. It is the home to the majority of Hungary's chemical industries receiving high wastewater loads from both industrial and municipal sources. The government seeks to clean up the river system, especially the Veszpremi-Sed River and Malom and Nador Channels, but is concerned about the costs of the chemical industry and the economically stressed municipalities and their customers. Local water and environmental authorities face the controversial challenge of satisfying the various demands on the system while taking into account constraints on both quality and supply. In this microcosm of Hungary and Central and Eastern Europe a water quality modeling and management tool developed by IIASA's Water Resources Project will be applied to help identify effective water quality management alternatives. This introductory Working Paper describes the nature of the water quality management problem, the policy setting and the management strategies which will be assessed