Heat kernel of integrable billiards in a magnetic field

We present analytical methods to calculate the magnetic response of non-interacting electrons constrained to a domain with boundaries and submitted to a uniform magnetic field. Two different methods of calculation are considered - one involving the large energy asymptotic expansion of the resolvent (Stewartson-Waechter method) is applicable to the case of separable systems, and another based on the small time asymptotic behaviour of the heat kernel (Balian-Bloch method). Both methods are in agreement with each other but differ from the result obtained previously by Robnik. Finally, the Balian-Bloch multiple scattering expansion is studied and the extension of our results to other geometries is discussed.Comment: 13 pages, Revte

Bayesian Conditioning, the Reflection Principle, and Quantum Decoherence

The probabilities a Bayesian agent assigns to a set of events typically change with time, for instance when the agent updates them in the light of new data. In this paper we address the question of how an agent's probabilities at different times are constrained by Dutch-book coherence. We review and attempt to clarify the argument that, although an agent is not forced by coherence to use the usual Bayesian conditioning rule to update his probabilities, coherence does require the agent's probabilities to satisfy van Fraassen's [1984] reflection principle (which entails a related constraint pointed out by Goldstein [1983]). We then exhibit the specialized assumption needed to recover Bayesian conditioning from an analogous reflection-style consideration. Bringing the argument to the context of quantum measurement theory, we show that "quantum decoherence" can be understood in purely personalist terms---quantum decoherence (as supposed in a von Neumann chain) is not a physical process at all, but an application of the reflection principle. From this point of view, the decoherence theory of Zeh, Zurek, and others as a story of quantum measurement has the plot turned exactly backward.Comment: 14 pages, written in memory of Itamar Pitowsk

The Origin of Degeneracies and Crossings in the 1d Hubbard Model

The paper is devoted to the connection between integrability of a finite quantum system and degeneracies of its energy levels. In particular, we analyze in detail the energy spectra of finite Hubbard chains. Heilmann and Lieb demonstrated that in these systems there are crossings of levels of the same parameter independent symmetry. We show that this apparent violation of the Wigner-von Neumann noncrossing rule follows directly from the existence of nontrivial conservation laws and is a characteristic signature of quantum integrability. The energy spectra of Hubbard chains display many instances of permanent (at all values of the coupling) twofold degeneracies that cannot be explained by parameter independent symmetries. We relate these degeneracies to the different transformation properties of the conserved currents under spatial reflections and the particle-hole transformation and estimate the fraction of doubly degenerate states. We also discuss multiply degenerate eigenstates of the Hubbard Hamiltonian. The wave functions of many of these states do not depend on the coupling, which suggests the existence of an additional parameter independent symmetry.Comment: 25 pages, 12 figure

The Behaviour Of Cosmological Models With Varying-G

We provide a detailed analysis of Friedmann-Robertson-Walker universes in a wide range of scalar-tensor theories of gravity. We apply solution-generating methods to three parametrised classes of scalar-tensor theory which lead naturally to general relativity in the weak-field limit. We restrict the parameters which specify these theories by the requirements imposed by the weak-field tests of gravitation theories in the solar system and by the requirement that viable cosmological solutions be obtained. We construct a range of exact solutions for open, closed, and flat isotropic universes containing matter with equation of state $p\leq \frac{1}{3}\rho$ and in vacuum. We study the range of early and late-time behaviours displayed, examine when there is a `bounce' at early times, and expansion maxima in closed models.Comment: 58 pages LaTeX, 6 postscript figures, uses eps

Mapping and assessment of ecosystems and their services. Urban ecosystems

Action 5 of the EU Biodiversity Strategy to 2020 requires member states to Map and Assess the state of Ecosystems and their Services (MAES). This report provides guidance for mapping and assessment of urban ecosystems. The MAES urban pilot is a collaboration between the European Commission, the European Environment Agency, volunteering Member States and cities, and stakeholders. Its ultimate goal is to deliver a knowledge base for policy and management of urban ecosystems by analysing urban green infrastructure, condition of urban ecosystems and ecosystem services. This report presents guidance for mapping urban ecosystems and includes an indicator framework to assess the condition of urban ecosystems and urban ecosystem services. The scientific framework of mapping and assessment is designed to support in particular urban planning policy and policy on green infrastructure at urban, metropolitan and regional scales. The results are based on the following different sources of information: a literature survey of 54 scientific articles, an online-survey (on urban ecosystems, related policies and planning instruments and with participation of 42 cities), ten case studies (Portugal: Cascais, Oeiras, Lisbon; Italy: Padua, Trento, Rome; The Netherlands: Utrecht; Poland: Poznań; Spain: Barcelona; Norway: Oslo), and a two-day expert workshop. The case studies constituted the core of the MAES urban pilot. They provided real examples and applications of how mapping and assessment can be organized to support policy; on top, they provided the necessary expertise to select a set of final indicators for condition and ecosystem services. Urban ecosystems or cities are defined here as socio-ecological systems which are composed of green infrastructure and built infrastructure. Urban green infrastructure (GI) is understood in this report as the multi-functional network of urban green spaces situated within the boundary of the urban ecosystem. Urban green spaces are the structural components of urban GI. This study has shown that there is a large scope for urban ecosystem assessments. Firstly, urban policies increasingly use urban green infrastructure and nature-based solutions in their planning process. Secondly, an increasing amount of data at multiple spatial scales is becoming available to support these policies, to provide a baseline, and to compare or benchmark cities with respect to the extent and management of the urban ecosystem. Concrete examples are given on how to delineate urban ecosystems, how to choose an appropriate spatial scale, and how to map urban ecosystems based on a combination of national or European datasets (including Urban Atlas) and locally collected information (e.g., location of trees). Also examples of typologies for urban green spaces are presented. This report presents an indicator framework which is composed of indicators to assess for urban ecosystem condition and for urban ecosystem services. These are the result of a rigorous selection process and ensure consistent mapping and assessment across Europe. The MAES urban pilot will continue with work on the interface between research and policy. The framework presented in this report needs to be tested and validated across Europe, e.g. on its applicability at city scale, on how far the methodology for measuring ecosystem condition and ecosystem service delivery in urban areas can be used to assess urban green infrastructure and nature-based solutions

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

Gender Differences of Shoppers in the Marketing and Management of Retail Agglomerations

This paper aims to: 1) identify gender differences in perception and evaluation of retail agglomerations and 2) discuss the implications of these differences for marketing and management. Based on a conceptual model we surveyed 2,151 agglomeration shoppers using interviewer-administered questionnaires. Structural equation modelling revealed that: accessibility, parking and infrastructure are perceived differently between gender groups. The attractiveness in terms of satisfaction, retention proneness and patronage intention were also evaluated distinctively. Nevertheless, when examining the impact of the perceived attributes on the agglomeration attractiveness there was no difference. In both settings the retail tenant mix and the atmosphere are the main antecedents of attractiveness. Finally, an importance performance analysis offers managers a method for prioritising their marketing efforts considering gender differences

Survey of highly non-Keplerian orbits with low-thrust propulsion

Celestial mechanics has traditionally been concerned with orbital motion under the action of a conservative gravitational potential. In particular, the inverse square gravitational force due to the potential of a uniform, spherical mass leads to a family of conic section orbits, as determined by Isaac Newton, who showed that Kepler‟s laws were derivable from his theory of gravitation. While orbital motion under the action of a conservative gravitational potential leads to an array of problems with often complex and interesting solutions, the addition of non-conservative forces offers new avenues of investigation. In particular, non-conservative forces lead to a rich diversity of problems associated with the existence, stability and control of families of highly non-Keplerian orbits generated by a gravitational potential and a non-conservative force. Highly non-Keplerian orbits can potentially have a broad range of practical applications across a number of different disciplines. This review aims to summarize the combined wealth of literature concerned with the dynamics, stability and control of highly non-Keplerian orbits for various low thrust propulsion devices, and to demonstrate some of these potential applications

Supply chain management resources, capabilities and execution

This paper identifies inter- and intra-organisational management resources that determine the level of execution of inter-firm alliance supply chain management (SCM). By drawing on network and resource-based view theories, a conceptual model proposes the effects of SCM resources and capabilities as influencing factors on SCM execution. The model was tested using survey data from studies conducted in two European supply chain environments. Variance-based structural equation modelling confirmed the hypothesised hierarchical order of three proposed antecedents: internal SCM resources affect joint SCM resources, which in turn influence collaborative SCM-related processes and finally SCM execution. An importance-performance analysis for both settings shows that providing and investing in internal SCM resources should be a priority when aiming to increase SCM execution. The theoretical contribution of this paper lies in confirming that the improvement of SCM execution follows a clear pathway featuring internal supply chain resources as one of the main drivers. The practical implications of this research include the development of a prioritisation list of measures that elevate SCM execution in the two country settings