Universal Cubic Eigenvalue Repulsion for Random Normal Matrices

Random matrix models consisting of normal matrices, defined by the sole constraint $[N^{\dag},N]=0$, will be explored. It is shown that cubic eigenvalue repulsion in the complex plane is universal with respect to the probability distribution of matrices. The density of eigenvalues, all correlation functions, and level spacing statistics are calculated. Normal matrix models offer more probability distributions amenable to analytical analysis than complex matrix models where only a model wth a Gaussian distribution are solvable. The statistics of numerically generated eigenvalues from gaussian distributed normal matrices are compared to the analytical results obtained and agreement is seen.Comment: 15 pages, 2 eps figures. to appar in Physical Review

Fredholm methods for billiard eigenfunctions in the coherent state representation

We obtain a semiclassical expression for the projector onto eigenfunctions by means of the Fredholm theory. We express the projector in the coherent state basis, thus obtaining the semiclassical Husimi representation of the stadium eigenfunctions, which is written in terms of classical invariants: periodic points, their monodromy matrices and Maslov indices.Comment: 12 pages, 10 figures. Submitted to Phys. Rev. E. Comments or questions to [email protected]

Identifying and prioritising services in European terrestrial and freshwater ecosystems

Ecosystems are multifunctional and provide humanity with a broad array of vital services. Effective management of services requires an improved evidence base, identifying the role of ecosystems in delivering multiple services, which can assist policy-makers in maintaining them. Here, information from the literature and scientific experts was used to systematically document the importance of services and identify trends in their use and status over time for the main terrestrial and freshwater ecosystems in Europe. The results from this review show that intensively managed ecosystems contribute mostly to vital provisioning services (e.g. agro-ecosystems provide food via crops and livestock, and forests provide wood), while semi-natural ecosystems (e.g. grasslands and mountains) are key contributors of genetic resources and cultural services (e.g. aesthetic values and sense of place). The most recent European trends in human use of services show increases in demand for crops from agro-ecosystems, timber from forests, water flow regulation from rivers, wetlands and mountains, and recreation and ecotourism in most ecosystems, but decreases in livestock production, freshwater capture fisheries, wild foods and virtually all services associated with ecosystems which have considerably decreased in area (e.g. semi-natural grasslands). The condition of the majority of services show either a degraded or mixed status across Europe with the exception of recent enhancements in timber production in forests and mountains, freshwater provision, water/erosion/natural hazard regulation and recreation/ecotourism in mountains, and climate regulation in forests. Key gaps in knowledge were evident for certain services across all ecosystems, including the provision of biochemicals and natural medicines, genetic resources and the regulating services of seed dispersal, pest/disease regulation and invasion resistance

Intrinsic decoherence and classical-quantum correspondence in two coupled delta-kicked rotors

We show that classical-quantum correspondence of center of mass motion in two coupled delta-kicked rotors can be obtained from intrinsic decoherence of the system itself which occurs due to the entanglement of the center of mass motion to the internal degree of freedom without coupling to external environment

Asymptotes in SU(2) Recoupling Theory: Wigner Matrices, 3j3j Symbols, and Character Localization

In this paper we employ a novel technique combining the Euler Maclaurin formula with the saddle point approximation method to obtain the asymptotic behavior (in the limit of large representation index $J$) of generic Wigner matrix elements $D^{J}_{MM'}(g)$. We use this result to derive asymptotic formulae for the character $\chi^J(g)$ of an SU(2) group element and for Wigner's $3j$ symbol. Surprisingly, given that we perform five successive layers of approximations, the asymptotic formula we obtain for $\chi^J(g)$ is in fact exact. This result provides a non trivial example of a Duistermaat-Heckman like localization property for discrete sums.Comment: 36 pages, 3 figure

A micro industry with closed energy and water cycles for sustainable rural development

Sustainable development requires combining economic viability with energy and environment conservation and ensuring social benefits. It is conceptualized that for designing a micro industry for sustainable rural industrialization, all these aspects should be integrated right up front. The concept includes; (a) utilization of local produce for value addition in a cluster of villages and enhancing income of the target population; (b) use of renewable energy and total utilization of energy generated by co and trigeneration (combining electric power production with heat utilization for heating and cooling); (c) conservation of water and complete recycling of effluents; (d) total utilization of all wastes for achieving closure towards a zero waste system. Enhanced economic viability and sustainability is achieved by integration of appropriate technologies into the industrial complex. To prove the concept, a model Micro Industrial Complex (MIC) has been set up in a semi arid desert region in Rajasthan, India at village Malunga in Jodhpur district. A biomass powered boiler and steam turbine system is used to generate 100-200 KVA of electric power and high energy steam for heating and cooling processes downstream. The unique feature of the equipment is a 100-150 kW back-pressure steam turbine, utilizing 3-4 tph (tonnes per hour) steam, developed by M/s IB Turbo. The biomass boiler raises steam at about 20 barg 3 tph, which is passed through a turbine to yield about 150 kW of electrical power. The steam let out at a back pressure of 1-3 barg has high exergy and this is passed on as thermal energy (about 2 MW), for use in various applications depending on the local produce and resources. The biomass fuel requirement for the boiler is 0.5-0.75 tph depending on its calorific value. In the current model, the electricity produced is used for running an oil expeller to extract castor oil and the castor cake is used as fuel in the boiler. The steam is used in a Multi Effect Distillation (MED) unit for drinking water production and in a Vapour Absorption Machine (VAM) for cooling, for banana ripening application. Additional steam is available for extraction of herbs such as mint and processing local vegetables. In this paper, we discuss the financial and economic viability of the system and show how the energy, water and materials are completely recycled and how the benefits are directed to the weaker sections of the community

Biophysical and sociocultural factors underlying spatial trade-offs of ecosystem services in semiarid watersheds

Biophysical and social systems are linked to form social-ecological systems whose sustainability depends on their capacity to absorb uncertainty and cope with disturbances. In this study, we explored the key biophysical and socio-cultural factors underlying ecosystem service supply in two semiarid watersheds of southern Spain. These included variables associated with the role that freshwater flows and biodiversity play in securing the system’s capacity to sustain essential ecosystem services and their relationship with social demand for services, local water governance, and land-use intensification. Our results reveal the importance of considering the invisible dimensions of water and biodiversity, i.e. green freshwater flows and trait-based indicators, because of their relevance to the supply of ecosystem services. Furthermore, they uncover the importance of traditional irrigation canals, a local water governance system, in maintaining the ecosystems’ capacity to supply services. The study also highlights the complex trade-offs that occur because of the spatial mismatch between ecosystem service supply (upstream) and ecosystem service demand (downstream) in watersheds. Finally, we found that land-use intensification generally resulted in losses of the biophysical factors that underpin the supply of some ecosystem services, increases in social demand for less diversified services, and the abandonment of local governance practices. Attempts to manage social-ecological systems toward sustainability at the local scale should identify the key biophysical and socio-cultural factors that are essential for maintaining ecosystem services and should recognize existing interrelationships between them. Land-use management should also take into account ecosystem service trade-offs and the consequences resulting from land-use intensificationFunding for the development of this research was provided by a postdoctoral grant from the Spanish National Institute for Agriculture and Food Research and Technology (INIA), which is cofunded by the Social European Fund; the Seventh Framework Programme of the European Commission (FP7, 2007-2013) under the BESAFE project (Biodiversity and Ecosystem Services: Arguments for our Future Environment, Contract No. 282743; http://www.besafe-project. net); and the OpenNESS Project (Operationalisation of Natural capital and Ecosystem Services: From Concepts to Real-World Applications, Contract No. 308428

Quenched Spin Tunneling and Diabolical Points in Magnetic Molecules: II. Asymmetric Configurations

The perfect quenching of spin tunneling first predicted for a model with biaxial symmetry, and recently observed in the magnetic molecule Fe_8, is further studied using the discrete phase integral (or Wentzel-Kramers-Brillouin) method. The analysis of the previous paper is extended to the case where the magnetic field has both hard and easy components, so that the Hamiltonian has no obvious symmetry. Herring's formula is now inapplicable, so the problem is solved by finding the wavefunction and using connection formulas at every turning point. A general formula for the energy surface in the vicinity of the diabolo is obtained in this way. This formula gives the tunneling apmplitude between two wells unrelated by symmetry in terms of a small number of action integrals, and appears to be generally valid, even for problems where the recursion contains more than five terms. Explicit results are obtained for the diabolical points in the model for Fe_8. These results exactly parallel the experimental observations. It is found that the leading semiclassical results for the diabolical points appear to be exact, and the points themselves lie on a perfect centered rectangular lattice in the magnetic field space. A variety of evidence in favor of this perfect lattice hypothesis is presented.Comment: Revtex; 4 ps figures; follow up to cond-mat/000311

Semiclassical Trace Formulas for Noninteracting Identical Particles

We extend the Gutzwiller trace formula to systems of noninteracting identical particles. The standard relation for isolated orbits does not apply since the energy of each particle is separately conserved causing the periodic orbits to occur in continuous families. The identical nature of the particles also introduces discrete permutational symmetries. We exploit the formalism of Creagh and Littlejohn [Phys. Rev. A 44, 836 (1991)], who have studied semiclassical dynamics in the presence of continuous symmetries, to derive many-body trace formulas for the full and symmetry-reduced densities of states. Numerical studies of the three-particle cardioid billiard are used to explicitly illustrate and test the results of the theory.Comment: 29 pages, 11 figures, submitted to PR