287 research outputs found

    Finite-dimensional Schwinger basis, deformed symmetries, Wigner function, and an algebraic approach to quantum phase

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    Schwinger's finite (D) dimensional periodic Hilbert space representations are studied on the toroidal lattice {\ee Z}_{D} \times {\ee Z}_{D} with specific emphasis on the deformed oscillator subalgebras and the generalized representations of the Wigner function. These subalgebras are shown to be admissible endowed with the non-negative norm of Hilbert space vectors. Hence, they provide the desired canonical basis for the algebraic formulation of the quantum phase problem. Certain equivalence classes in the space of labels are identified within each subalgebra, and connections with area-preserving canonical transformations are examined. The generalized representations of the Wigner function are examined in the finite-dimensional cyclic Schwinger basis. These representations are shown to conform to all fundamental conditions of the generalized phase space Wigner distribution. As a specific application of the Schwinger basis, the number-phase unitary operator pair in {\ee Z}_{D} \times {\ee Z}_{D} is studied and, based on the admissibility of the underlying q-oscillator subalgebra, an {\it algebraic} approach to the unitary quantum phase operator is established. This being the focus of this work, connections with the Susskind-Glogower- Carruthers-Nieto phase operator formalism as well as standard action-angle Wigner function formalisms are examined in the infinite-period limit. The concept of continuously shifted Fock basis is introduced to facilitate the Fock space representations of the Wigner function.Comment: 19 pages, no figure

    Does landscape-scale conservation management enhance the provision of ecosystem services?

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    Biodiversity conservation approaches are increasingly being implemented at the landscape-scale to support the maintenance of metapopulations and metacommunities. However, the impact of such interventions on the provision of ecosystem services is less well defined. Here we examine the potential impacts of landscape-scale conservation initiatives on ecosystem services, through analysis of five case study areas in England and Wales. The provision of multiple ecosystem services was projected according to current management plans and compared with a baseline scenario. Multicriteria analysis indicated that in most cases landscape-scale approaches lead to an overall increase in service provision. Consistent increases were projected in carbon storage, recreation and aesthetic value, as well as biodiversity value. However, most study areas provided evidence of trade-offs, particularly between provisioning services and other types of service. Results differed markedly between study areas, highlighting the importance of local context. These results suggest that landscape-scale conservation approaches are likely to be effective in increasing ecosystem service provision, but also indicate that associated costs can be significant, particularly in lowland areas

    Multicomplementary operators via finite Fourier transform

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    A complete set of d+1 mutually unbiased bases exists in a Hilbert spaces of dimension d, whenever d is a power of a prime. We discuss a simple construction of d+1 disjoint classes (each one having d-1 commuting operators) such that the corresponding eigenstates form sets of unbiased bases. Such a construction works properly for prime dimension. We investigate an alternative construction in which the real numbers that label the classes are replaced by a finite field having d elements. One of these classes is diagonal, and can be mapped to cyclic operators by means of the finite Fourier transform, which allows one to understand complementarity in a similar way as for the position-momentum pair in standard quantum mechanics. The relevant examples of two and three qubits and two qutrits are discussed in detail.Comment: 15 pages, no figure

    Quasiprobability distribution functions for finite-dimensional discrete phase spaces: Spin-tunneling effects in a toy model

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    We show how quasiprobability distribution functions defined over N2N^{2}-dimensional discrete phase spaces can be used to treat physical systems described by a finite space of states which exhibit spin tunneling effects. This particular approach is then applied to the Lipkin-Meshkov-Glick model in order to obtain the time evolution of the discrete Husimi function, and as a by-product the energy gap for a symmetric combination of ground and first excited states. Moreover, we also show how an angle-based potential approach can be efficiently employed to explain qualitatively certain features of the energy gap in terms of a spin tunneling. Entropy functionals are also discussed in this context. Such results reinforce not only the formalism per se but also the possibility of some future potential applications in other branches of physics.Comment: 7 pages, 8 figures, title modified, new setences and references included, to appear in Physical Review

    Reconstructing past ecological networks: the reconfiguration of seed-dispersal interactions after megafaunal extinction

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    The late Quaternary megafaunal extinction impacted ecological communities worldwide, and affected key ecological processes such as seed dispersal. The traits of several species of large-seeded plants are thought to have evolved in response to interactions with extinct megafauna, but how these extinctions affected the organization of interactions in seed-dispersal systems is poorly understood. Here, we combined ecological and paleontological data and network analyses to investigate how the structure of a species-rich seed-dispersal network could have changed from the Pleistocene to the present and examine the possible consequences of such changes. Our results indicate that the seed-dispersal network was organized into modules across the different time periods but has been reconfigured in different ways over time. The episode of megafaunal extinction and the arrival of humans changed how seed dispersers were distributed among network modules. However, the recent introduction of livestock into the seed-dispersal system partially restored the original network organization by strengthening the modular configuration. Moreover, after megafaunal extinctions, introduced species and some smaller native mammals became key components for the structure of the seed-dispersal network. We hypothesize that such changes in network structure affected both animal and plant assemblages, potentially contributing to the shaping of modern ecological communities. The ongoing extinction of key large vertebrates will lead to a variety of context-dependent rearranged ecological networks, most certainly affecting ecological and evolutionary processes.We thank D. M. Hansen, P. Jordano and two anonymous reviewers for critical suggestions regards the manuscript. M. M. P., M. G. and P. R. G. were supported by São Paulo Research Foundation (FAPESP; grant nos. 2009/54422-8, 2004/00810-3, 2008/10154-7, and 2009/54567-6). C. I. D. was supported by Stanford University. M. G ., P. R . G . and M. A . P. receive research grants from CNPq. We also thank the Earthwatch Institute and Conservation International for financial support and Conservation International, Lucas Leuzinger and Marina Schweizer for their permission to work on their properties

    The hadron-quark phase transition in dense matter and neutron stars

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    We study the hadron-quark phase transition in the interior of neutron stars (NS's). We calculate the equation of state (EOS) of hadronic matter using the Brueckner-Bethe-Goldstone formalism with realistic two-body and three-body forces, as well as a relativistic mean field model. For quark matter we employ the MIT bag model constraining the bag constant by using the indications coming from the recent experimental results obtained at the CERN SPS on the formation of a quark-gluon plasma. We find necessary to introduce a density dependent bag parameter, and the corresponding consistent thermodynamical formalism. We calculate the structure of NS interiors with the EOS comprising both phases, and we find that the NS maximum masses fall in a relatively narrow interval, 1.4M⊙≤Mmax≤1.7M⊙1.4 M_\odot \leq M_{\rm max} \leq 1.7 M_\odot. The precise value of the maximum mass turns out to be only weakly correlated with the value of the energy density at the assumed transition point in nearly symmetric nuclear matter.Comment: 25 pages, Revtex4, 16 figures included as postscrip
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