N-complexes as functors, amplitude cohomology and fusion rules

We consider N-complexes as functors over an appropriate linear category in order to show first that the Krull-Schmidt Theorem holds, then to prove that amplitude cohomology only vanishes on injective functors providing a well defined functor on the stable category. For left truncated N-complexes, we show that amplitude cohomology discriminates the isomorphism class up to a projective functor summand. Moreover amplitude cohomology of positive N-complexes is proved to be isomorphic to an Ext functor of an indecomposable N-complex inside the abelian functor category. Finally we show that for the monoidal structure of N-complexes a Clebsch-Gordan formula holds, in other words the fusion rules for N-complexes can be determined.Comment: Final versio

Duality between quantum symmetric algebras

Using certain pairings of couples, we obtain a large class of two-sided non-degenerated graded Hopf pairings for quantum symmetric algebras.Comment: 15 pages. Letters in Math. Phy., to appear soo

Spin-Boson Hamiltonian and Optical Absorption of Molecular Dimers

An analysis of the eigenstates of a symmetry-broken spin-boson Hamiltonian is performed by computing Bloch and Husimi projections. The eigenstate analysis is combined with the calculation of absorption bands of asymmetric dimer configurations constituted by monomers with nonidentical excitation energies and optical transition matrix elements. Absorption bands with regular and irregular fine structures are obtained and related to the transition from the coexistence to a mixing of adiabatic branches in the spectrum. It is shown that correlations between spin states allow for an interpolation between absorption bands for different optical asymmetries.Comment: 15 pages, revTeX, 8 figures, accepted for publication in Phys. Rev.

Impact of Grazing Management on the Productivity of Cold Temperate Grasslands of Southern Patagonia - A Critical Assessment

The contention that productivity of cold temperate grasslands of southern Patagonia have been greatly affected by domestic herbivore grazing in the past is fairly widespread. The consequences of spatiotemporal interactions between grazing and abiotic factors on the overall productivity of such systems, however, are still poorly understood. Predictions of both short- and long-term impacts of grazing management strategies on grassland productivity require a better understanding of these interactions. In this paper we make a critical assessment of the impact of grazing management on long-term sustainability of the grass steppes of southern Patagonia (Argentina). We discuss this issue in the context of current understanding of structure and function of these grass steppes, and of present-day global change concerns. We explore the capabilities of present-day tools to integrate biotic and abiotic factors at the landscape level to improve grazing management decisions

A generalization of Gabriel's Galois covering functors II: 2-categorical Cohen-Montgomery duality

Given a group $G$, we define suitable 2-categorical structures on the class of all small categories with $G$-actions and on the class of all small $G$-graded categories, and prove that 2-categorical extensions of the orbit category construction and of the smash product construction turn out to be 2-equivalences (2-quasi-inverses to each other), which extends the Cohen-Montgomery duality.Comment: 31 pages. I moved the Sec of G-GrCat into Sec 3, and added Lem 5.6. I added more explanations in the proof of Cor 7.6 with (7.5). I added Def 7.7 and Lem 7.8 with the necessary additional assumptions in Props 7.9 and 7.11. I added Lem 8.8 with a short proof, Rmk 8.9 and the proof of Lem 8.10. The final publication is available at Springer via http://dx.doi.org/10.1007/s10485-015-9416-

Quantum groups and double quiver algebras

For a finite dimensional semisimple Lie algebra ${\frak{g}}$ and a root $q$ of unity in a field $k,$ we associate to these data a double quiver $\bar{\cal{Q}}.$ It is shown that a restricted version of the quantized enveloping algebras $U_q(\frak g)$ is a quotient of the double quiver algebra $k\bar{\cal Q}.$Comment: 15 page

Integrability and action operators in quantum Hamiltonian systems

For a (classically) integrable quantum mechanical system with two degrees of freedom, the functional dependence $\hat{H}=H_Q(\hat{J}_1,\hat{J}_2)$ of the Hamiltonian operator on the action operators is analyzed and compared with the corresponding functional relationship $H(p_1,q_1;p_2,q_2) = H_C(J_1,J_2)$ in the classical limit of that system. The former is shown to converge toward the latter in some asymptotic regime associated with the classical limit, but the convergence is, in general, non-uniform. The existence of the function $\hat{H}=H_Q(\hat{J}_1,\hat{J}_2)$ in the integrable regime of a parametric quantum system explains empirical results for the dimensionality of manifolds in parameter space on which at least two levels are degenerate. The comparative analysis is carried out for an integrable one-parameter two-spin model. Additional results presented for the (integrable) circular billiard model illuminate the same conclusions from a different angle.Comment: 9 page

Flow equations for Hamiltonians: Contrasting different approaches by using a numerically solvable model

To contrast different generators for flow equations for Hamiltonians and to discuss the dependence of physical quantities on unitarily equivalent, but effectively different initial Hamiltonians, a numerically solvable model is considered which is structurally similar to impurity models. By this we discuss the question of optimization for the first time. A general truncation scheme is established that produces good results for the Hamiltonian flow as well as for the operator flow. Nevertheless, it is also pointed out that a systematic and feasible scheme for the operator flow on the operator level is missing. For this, an explicit analysis of the operator flow is given for the first time. We observe that truncation of the series of the observable flow after the linear or bilinear terms does not yield satisfactory results for the entire parameter regime as - especially close to resonances - even high orders of the exact series expansion carry considerable weight.Comment: 25 pages, 10 figure

Prólogo

Con mucho agrado ponemos a disposición de la comunidad científica, los artículos completos de los trabajos presentados en el VII Congreso de Ecología y Manejo de Ecosistemas Acuáticos Pampeanos (EMEAP 7), que se realizó el 19 y 20 de septiembre de 2013 organizado por las cátedras de Acuicultura y Ecología de la Facultad de Agronomía y Veterinaria de la Universidad Nacional de Río Cuarto (Argentina). En este evento, que contó con la asistencia de unos ciento sesenta investigadores y alumnos, se expusieron ciento dieciséis trabajos representando a veintiséis universidades e institutos de las provincias de Buenos Aires, La Pampa, Córdoba, San Luis, Corrientes, Entre Ríos y Salta.Facultad de Ciencias Naturales y Muse

Prólogo

Con mucho agrado ponemos a disposición de la comunidad científica, los artículos completos de los trabajos presentados en el VII Congreso de Ecología y Manejo de Ecosistemas Acuáticos Pampeanos (EMEAP 7), que se realizó el 19 y 20 de septiembre de 2013 organizado por las cátedras de Acuicultura y Ecología de la Facultad de Agronomía y Veterinaria de la Universidad Nacional de Río Cuarto (Argentina). En este evento, que contó con la asistencia de unos ciento sesenta investigadores y alumnos, se expusieron ciento dieciséis trabajos representando a veintiséis universidades e institutos de las provincias de Buenos Aires, La Pampa, Córdoba, San Luis, Corrientes, Entre Ríos y Salta.Facultad de Ciencias Naturales y Muse