4,101 research outputs found
Multipliers for p-Bessel sequences in Banach spaces
Multipliers have been recently introduced as operators for Bessel sequences
and frames in Hilbert spaces. These operators are defined by a fixed
multiplication pattern (the symbol) which is inserted between the analysis and
synthesis operators. In this paper, we will generalize the concept of Bessel
multipliers for p-Bessel and p-Riesz sequences in Banach spaces. It will be
shown that bounded symbols lead to bounded operators. Symbols converging to
zero induce compact operators. Furthermore, we will give sufficient conditions
for multipliers to be nuclear operators. Finally, we will show the continuous
dependency of the multipliers on their parameters.Comment: 17 page
Frame-Related Sequences in Chains and Scales of Hilbert Spaces
Frames for Hilbert spaces are interesting for mathematicians but also important for applications in, e.g., signal analysis and physics. In both mathematics and physics, it is natural to consider a full scale of spaces, and not only a single one. In this paper, we study how certain frame-related properties of a certain sequence in one of the spaces, such as completeness or the property of being a (semi-) frame, propagate to the other ones in a scale of Hilbert spaces. We link that to the properties of the respective frame-related operators, such as analysis or synthesis. We start with a detailed survey of the theory of Hilbert chains. Using a canonical isomorphism, the properties of frame sequences are naturally preserved between different spaces. We also show that some results can be transferred if the original sequence is considered—in particular, that the upper semi-frame property is kept in larger spaces, while the lower one is kept in smaller ones. This leads to a negative result: a sequence can never be a frame for two Hilbert spaces of the scale if the scale is non-trivial, i.e., if the spaces are not equal
Epoch Dependent Dark Energy
We present a model in which the equation of state parameter w approaches -1
near a particular value of z, and has significant negative values in a
restricted range of z. For example, one can have w ~ -1 near z = 1, and w >
-0.2 from z = 0 to z = 0.3, and for z > 9. The ingredients of the model are
neutral fermions (which may be neutrinos, neutralinos, etc) which are very
weakly coupled to a light scalar field. This model emphasises the importance of
the proposed studies of the properties of dark energy into the region z > 1.Comment: 7pp., 2 figs. Invited talk at the 5th Int'l. Wkshp. on the Dark Side
of the Universe, 1-5 June 2009 Melbourne, DSU09; to appear in the proceeding
Simulating noisy quantum protocols with quantum trajectories
The theory of quantum trajectories is applied to simulate the effects of
quantum noise sources induced by the environment on quantum information
protocols. We study two models that generalize single qubit noise channels like
amplitude damping and phase flip to the many-qubit situation. We calculate the
fidelity of quantum information transmission through a chaotic channel using
the teleportation scheme with different environments. In this example, we
analyze the role played by the kind of collective noise suffered by the quantum
processor during its operation. We also investigate the stability of a quantum
algorithm simulating the quantum dynamics of a paradigmatic model of chaos, the
baker's map. Our results demonstrate that, using the quantum trajectories
approach, we are able to simulate quantum protocols in the presence of noise
and with large system sizes of more than 20 qubits.Comment: 11 pages, 7 fig
Unusual Higgs or Supersymmetry from Natural Electroweak Symmetry Breaking
This review provides an elementary discussion of electroweak symmetry
breaking in the minimal and the next-to-minimal supersymmetric models with the
focus on the fine-tuning problem -- the tension between natural electroweak
symmetry breaking and the direct search limit on the Higgs boson mass. Two
generic solutions of the fine-tuning problem are discussed in detail: models
with unusual Higgs decays; and models with unusual pattern of soft
supersymmetry breaking parameters.Comment: 23 pages, 6 figures; invited review by MPL
Generalized Froggatt-Nielsen Mechanism
In this paper, we propose a Generalized Froggatt-Nielsen mechanism in which
non-renormalizable operators involving a GUT group and non-singlet
Higgs field are introduced. Thus the GUT gauge symmetry breaking and the
generation of hierarchical flavor hierarchy have a common origin in this
mechanism. In this Generalized Froggatt-Nielsen mechanism, we propose
universality conditions for coefficients corresponding to different
contractions in the group productions. We find that the predictions in
Generalized Froggatt-Nielsen mechanism for SU(5) GUT is different to that of
ordinary Froggatt-Nielsen mechanism. Such Generalized Froggatt-Nielsen
mechanism can be used in GUT models when ordinary Froggatt-Nielsen mechanism is
no longer available. We study the application of Generalized Froggatt-Nielsen
mechanism in SO(10) model. We find that realistic standard model mass hierarchy
and mixings can be obtained both in SU(5) and SO(10) GUT models with such
Generalized Froggatt-Nielsen mechanism.Comment: 4 pages, no figure
Frame Theory for Signal Processing in Psychoacoustics
This review chapter aims to strengthen the link between frame theory and
signal processing tasks in psychoacoustics. On the one side, the basic concepts
of frame theory are presented and some proofs are provided to explain those
concepts in some detail. The goal is to reveal to hearing scientists how this
mathematical theory could be relevant for their research. In particular, we
focus on frame theory in a filter bank approach, which is probably the most
relevant view-point for audio signal processing. On the other side, basic
psychoacoustic concepts are presented to stimulate mathematicians to apply
their knowledge in this field
Detecting a light Higgs boson at the Fermilab Tevatron through enhanced decays to photon pairs
We analyze the prospects of the Tevatron for finding a Higgs boson in the two
photon decay mode. We conclude that the Standard Model (SM) Higgs boson will
likely not be discovered in this mode. However, we motivate several theories
beyond the SM, including the MSSM, that predict a Higgs boson with enhanced
branching fractions into photons, and calculate the luminosity needed to
discover a general Higgs boson at the Tevatron by a two-photon invariant mass
peak at large transverse momentum. We find that a high luminosity Tevatron will
play a significant role in discovering or constraining these theories.Comment: 20 pages, latex, 5 figure
Monte Carlo simulations of random copolymers at a selective interface
We investigate numerically using the bond--fluctuation model the adsorption
of a random AB--copolymer at the interface between two solvents. From our
results we infer several scaling relations: the radius of gyration of the
copolymer in the direction perpendicular to the interface () scales
with , the interfacial selectivity strength, as
where is the usual Flory exponent and
is the copolymer's length; furthermore the monomer density at the interface
scales as for small . We also determine numerically the
monomer densities in the two solvents and discuss their dependence on the
distance from the interface.Comment: Latex text file appended with figures.tar.g
Semiclassical properties and chaos degree for the quantum baker's map
We study the chaotic behaviour and the quantum-classical correspondence for
the baker's map. Correspondence between quantum and classical expectation
values is investigated and it is numerically shown that it is lost at the
logarithmic timescale. The quantum chaos degree is computed and it is
demonstrated that it describes the chaotic features of the model. The
correspondence between classical and quantum chaos degrees is considered.Comment: 30 pages, 4 figures, accepted for publication in J. Math. Phy
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