Positive definite ∗*-spherical functions, property (T), and C∗C^*-completions of Gelfand pairs

The study of existence of a universal $C^*$-completion of the $^*$-algebra canonically associated to a Hecke pair was initiated by Hall, who proved that the Hecke algebra associated to (\operatorname{SL}_2(\Qp), \operatorname{SL}_2(\Zp)) does not admit a universal $C^*$-completion. Kaliszewski, Landstad and Quigg studied the problem by placing it in the framework of Fell-Rieffel equivalence, and highlighted the role of other $C^*$-completions. In the case of the pair (\operatorname{SL}_n(\Qp), \operatorname{SL}_n(\Zp)) for $n\geq 3$ we show, invoking property (T) of \operatorname{SL}_n(\Qp), that the $C^*$-completion of the $L^1$-Banach algebra and the corner of C^*(\operatorname{SL}_n(\Qp)) determined by the subgroup are distinct. In fact, we prove a more general result valid for a simple algebraic group of rank at least $2$ over a $\mathfrak{p}$-adic field with a good choice of a maximal compact open subgroup.Comment: 15 page

Gauge-Higgs unification on the brane

From the quantum field theory point of view, matter and gauge fields are generally expected to be localised around branes or topological defects occurring in extra dimensions. Here I discuss a simple scenario where, by starting with a five dimensional SU(3) gauge theory, we end up with several 4-D parallel branes with localised "chiral" fermions and gauge fields to them. I will show that it is possible to reproduce the electroweak model confined to a single brane, allowing a simple and geometrical approach to the fermion hierarchy problem. Some nice results of this construction are: Gauge and Higgs fields are unified at the 5-D level; and new particles are predicted: a left-handed neutrino of zero hypercharge, and a massive vector field coupling together the new neutrino to other left-handed leptons.Comment: Contribution to the proceedings of the RTN workshop "The Quest for Unification: Theory Confronts Experiment", Corfu, Greece, Sept 11-18, 200

Normal form decomposition for Gaussian-to-Gaussian superoperators

In this paper we explore the set of linear maps sending the set of quantum Gaussian states into itself. These maps are in general not positive, a feature which can be exploited as a test to check whether a given quantum state belongs to the convex hull of Gaussian states (if one of the considered maps sends it into a non positive operator, the above state is certified not to belong to the set). Generalizing a result known to be valid under the assumption of complete positivity, we provide a characterization of these Gaussian-to-Gaussian (not necessarily positive) superoperators in terms of their action on the characteristic function of the inputs. For the special case of one-mode mappings we also show that any Gaussian-to-Gaussian superoperator can be expressed as a concatenation of a phase-space dilatation, followed by the action of a completely positive Gaussian channel, possibly composed with a transposition. While a similar decomposition is shown to fail in the multi-mode scenario, we prove that it still holds at least under the further hypothesis of homogeneous action on the covariance matrix

On the origin of <i>Halipeurus heraldicus</i> on Round Island petrels: cophylogenetic relationships between petrels and their chewing lice

Lice phylogenetic relationships have often been used to elucidate host relationships and vice versa. In this study, we investigate the louse genus Halipeurus which parasitizes bird hosts in the families Procellariidae, Hydrobatidae and Pelecanoididae. The presence of two lice species on Pterodroma arminjoniana in different breeding grounds (Halipeurus heraldicus on Round Island, off Mauritius in the Indian Ocean and Halipeurus kermadecensis on Trindade Island in the Atlantic Ocean) has led to some confusion in the distribution of Pt. arminjoniana and its close relatives Pt. heraldica and Pt. neglecta. By using a cophylogenetic approach that incorporates uncertainties in phylogenetic reconstructions, we show significant overall coevolution between Halipeurus lice and their hosts. However, the study also indicates that the presence of H. heraldicus on Pt. arminjoniana and Pt. neglecta on Round Island and on Pt. heraldica on Gambier Island are the result of a host switch whereas H. kermadecensis is the ancestral parasite of Pt. arminjoniana. This suggests that H. kermadecensis was lost during or after colonisation of Round Island by Pt. arminjoniana. We conclude that cophylogenetic analyses are central to inferring the evolutionary history and biogeographical patterns of hosts and their parasites

Quantum state transfer in imperfect artificial spin networks

High-fidelity quantum computation and quantum state transfer are possible in short spin chains. We exploit a system based on a dispersive qubit-boson interaction to mimic XY coupling. In this model, the usually assumed nearest-neighbors coupling is no more valid: all the qubits are mutually coupled. We analyze the performances of our model for quantum state transfer showing how pre-engineered coupling rates allow for nearly optimal state transfer. We address a setup of superconducting qubits coupled to a microstrip cavity in which our analysis may be applied.Comment: 4 pages, 3 figures, RevTeX

Landauer's principle in multipartite open quantum system dynamics

We investigate the link between information and thermodynamics embodied by Landauer's principle in the open dynamics of a multipartite quantum system. Such irreversible dynamics is described in terms of a collisional model with a finite temperature reservoir. We demonstrate that Landauer's principle holds, for such a configuration, in a form that involves the flow of heat dissipated into the environment and the rate of change of the entropy of the system. Quite remarkably, such a principle for {\it heat and entropy power} can be explicitly linked to the rate of creation of correlations among the elements of the multipartite system and, in turn, the non-Markovian nature of their reduced evolution. Such features are illustrated in two exemplary cases.Comment: 5 pages, 3 figures, RevTeX4-1; Accepted for publication in Phys. Rev. Let

Extraction of Singlet States from Noninteracting High-Dimensional Spins

We present a scheme for the extraction of singlet states of two remote particles of arbitrary quantum spin number. The goal is achieved through post-selection of the state of interaction mediators sent in succession. A small number of iterations is sufficient to make the scheme effective. We propose two suitable experimental setups where the protocol can be implemented.Comment: 4 pages, 2 figure

Integrating a finantial module in the Web-Ecoyield-SAFE model for bioeconomic assessment of agroforestry systems

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