Completely integrable systems: a generalization

We present a slight generalization of the notion of completely integrable systems to get them being integrable by quadratures. We use this generalization to integrate dynamical systems on double Lie groups.Comment: Latex, 15 page

Construction of completely integrable systems by Poisson mappings

Pulling back sets of functions in involution by Poisson mappings and adding Casimir functions during the process allows to construct completely integrable systems. Some examples are investigated in detail.Comment: AmsTeX, 9 page

Contractions: Nijenhuis and Saletan tensors for general algebraic structures

Generalizations in many directions of the contraction procedure for Lie algebras introduced by E.J.Saletan are proposed. Products of arbitrary nature, not necessarily Lie brackets, are considered on sections of finite-dimensional vector bundles. Saletan contractions of such infinite-dimensional algebras are obtained via a generalization of the Nijenhuis tensor approach. In particular, this procedure is applied to Lie algebras, Lie algebroids, and Poisson structures. There are also results on contractions of n-ary products and coproducts.Comment: 25 pages, LateX, corrected typo

Generalized n-Poisson brackets on a symplectic manifold

On a symplectic manifold a family of generalized Poisson brackets associated with powers of the symplectic form is studied. The extreme cases are related to the Hamiltonian and Liouville dynamics. It is shown that the Dirac brackets can be obtained in a similar way.Comment: Latex, 10 pages, to appear in Mod. Phys. Lett.

Noncommutative differential calculus for Moyal subalgebras

We build a differential calculus for subalgebras of the Moyal algebra on R^4 starting from a redundant differential calculus on the Moyal algebra, which is suitable for reduction. In some cases we find a frame of 1-forms which allows to realize the complex of forms as a tensor product of the noncommutative subalgebras with the external algebra Lambda^*.Comment: 13 pages, no figures. One reference added, minor correction

A variational principle for volume-preserving dynamics

We provide a variational description of any Liouville (i.e. volume preserving) autonomous vector fields on a smooth manifold. This is obtained via a ``maximal degree'' variational principle; critical sections for this are integral manifolds for the Liouville vector field. We work in coordinates and provide explicit formulae

On Turing dynamical systems and the Atiyah problem

Main theorems of the article concern the problem of M. Atiyah on possible values of l^2-Betti numbers. It is shown that all non-negative real numbers are l^2-Betti numbers, and that "many" (for example all non-negative algebraic) real numbers are l^2-Betti numbers of simply connected manifolds with respect to a free cocompact action. Also an explicit example is constructed which leads to a simply connected manifold with a transcendental l^2-Betti number with respect to an action of the threefold direct product of the lamplighter group Z/2 wr Z. The main new idea is embedding Turing machines into integral group rings. The main tool developed generalizes known techniques of spectral computations for certain random walk operators to arbitrary operators in groupoid rings of discrete measured groupoids.Comment: 35 pages; essentially identical to the published versio

Thermal transport of the XXZ chain in a magnetic field

We study the heat conduction of the spin-1/2 XXZ chain in finite magnetic fields where magnetothermal effects arise. Due to the integrability of this model, all transport coefficients diverge, signaled by finite Drude weights. Using exact diagonalization and mean-field theory, we analyze the temperature and field dependence of the thermal Drude weight for various exchange anisotropies under the condition of zero magnetization-current flow. First, we find a strong magnetic field dependence of the Drude weight, including a suppression of its magnitude with increasing field strength and a non-monotonic field-dependence of the peak position. Second, for small exchange anisotropies and magnetic fields in the massless as well as in the fully polarized regime the mean-field approach is in excellent agreement with the exact diagonalization data. Third, at the field-induced quantum critical line between the para- and ferromagnetic region we propose a universal low-temperature behavior of the thermal Drude weight.Comment: 9 pages REVTeX4 including 5 figures, revised version, refs. added, typos correcte

On the structure of the body of states with positive partial transpose

We show that the convex set of separable mixed states of the 2 x 2 system is a body of constant height. This fact is used to prove that the probability to find a random state to be separable equals 2 times the probability to find a random boundary state to be separable, provided the random states are generated uniformly with respect to the Hilbert-Schmidt (Euclidean) distance. An analogous property holds for the set of positive-partial-transpose states for an arbitrary bipartite system.Comment: 10 pages, 1 figure; ver. 2 - minor changes, new proof of lemma

The Influence of Medicare Home Health Payment Incentives: Does Payer Source Matter?

During the late 1990s, an interim payment system (IPS) was instituted to constrain Medicare home health care expenditures. Previous research has largely focused on the implications of the IPS for Medicare patients, but our study broadens the analysis to consider patients with other payer sources. Using the National Home and Hospice Care Survey, we found similar effects of the IPS across payer types. Specifically, the IPS was associated with a decrease in access to care for the sickest patients, less agency assistance with activities of daily living, and shorter length-of-use. However, these changes did not translate into worse discharge outcomes.Medicare, health, incentives