18,912 research outputs found
Positive definite -spherical functions, property (T), and -completions of Gelfand pairs
The study of existence of a universal -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 -completion.
Kaliszewski, Landstad and Quigg studied the problem by placing it in the
framework of Fell-Rieffel equivalence, and highlighted the role of other
-completions. In the case of the pair (\operatorname{SL}_n(\Qp),
\operatorname{SL}_n(\Zp)) for we show, invoking property (T) of
\operatorname{SL}_n(\Qp), that the -completion of the -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 over a -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.
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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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