2,876,506 research outputs found
The Unified Method: III Non-Linearizable Problems on the Interval
Boundary value problems for integrable nonlinear evolution PDEs formulated on
the finite interval can be analyzed by the unified method introduced by one of
the authors and used extensively in the literature. The implementation of this
general method to this particular class of problems yields the solution in
terms of the unique solution of a matrix Riemann-Hilbert problem formulated in
the complex -plane (the Fourier plane), which has a jump matrix with
explicit -dependence involving six scalar functions of , called
spectral functions. Two of these functions depend on the initial data, whereas
the other four depend on all boundary values. The most difficult step of the
new method is the characterization of the latter four spectral functions in
terms of the given initial and boundary data, i.e. the elimination of the
unknown boundary values. Here, we present an effective characterization of the
spectral functions in terms of the given initial and boundary data. We present
two different characterizations of this problem. One is based on the analysis
of the so-called global relation, on the analysis of the equations obtained
from the global relation via certain transformations leaving the dispersion
relation of the associated linearized PDE invariant, and on the computation of
the large asymptotics of the eigenfunctions defining the relevant spectral
functions. The other is based on the analysis of the global relation and on the
introduction of the so-called Gelfand-Levitan-Marchenko representations of the
eigenfunctions defining the relevant spectral functions. We also show that
these two different characterizations are equivalent and that in the limit when
the length of the interval tends to infinity, the relevant formulas reduce to
the analogous formulas obtained recently for the case of boundary value
problems formulated on the half-line.Comment: 22 page
Constraints on Cold Dark Matter Accelerating Cosmologies and Cluster Formation
We discuss the properties of homogeneous and isotropic flat cosmologies in
which the present accelerating stage is powered only by the gravitationally
induced creation of cold dark matter (CCDM) particles (). For
some matter creation rates proposed in the literature, we show that the main
cosmological functions such as the scale factor of the universe, the Hubble
expansion rate, the growth factor and the cluster formation rate are
analytically defined. The best CCDM scenario has only one free parameter and
our joint analysis involving BAO + CMB + SNe Ia data yields
() where
is the observed matter density parameter. In particular, this implies that the
model has no dark energy but the part of the matter that is effectively
clustering is in good agreement with the latest determinations from large scale
structure. The growth of perturbation and the formation of galaxy clusters in
such scenarios are also investigated. Despite the fact that both scenarios may
share the same Hubble expansion, we find that matter creation cosmologies
predict stronger small scale dynamics which implies a faster growth rate of
perturbations with respect to the usual CDM cosmology. Such results
point to the possibility of a crucial observational test confronting CCDM with
CDM scenarios trough a more detailed analysis involving CMB, weak
lensing, as well as the large scale structure.Comment: 12 pages, 3 figures, Accepted for publication by Physical Rev.
Tunable coupling in circuit quantum electrodynamics with a superconducting V-system
Recent progress in superconducting qubits has demonstrated the potential of
these devices for the future of quantum information processing. One desirable
feature for quantum computing is independent control of qubit interactions as
well as qubit energies. We demonstrate a new type of superconducting charge
qubit that has a V-shaped energy spectrum and uses quantum interference to
provide independent control over the qubit energy and dipole coupling to a
superconducting cavity. We demonstrate dynamic access to the strong coupling
regime by tuning the coupling strength from less than 200 kHz to more than 40
MHz. This tunable coupling can be used to protect the qubit from cavity-induced
relaxation and avoid unwanted qubit-qubit interactions in a multi-qubit system.Comment: 5 pages, 4 figure
Discrete breathers in systems with homogeneous potentials - analytic solutions
We construct lattice Hamiltonians with homogeneous interaction potentials
which allow for explicit breather solutions. Especially we obtain exponentially
localized solutions for -dimensional lattices with .Comment: 10 page
New Cosmic Accelerating Scenario without Dark Energy
We propose an alternative, nonsingular, cosmic scenario based on
gravitationally induced particle production. The model is an attempt to evade
the coincidence and cosmological constant problems of the standard model
(CDM) and also to connect the early and late time accelerating stages
of the Universe. Our space-time emerges from a pure initial de Sitter stage
thereby providing a natural solution to the horizon problem. Subsequently, due
to an instability provoked by the production of massless particles, the
Universe evolves smoothly to the standard radiation dominated era thereby
ending the production of radiation as required by the conformal invariance.
Next, the radiation becomes sub-dominant with the Universe entering in the cold
dark matter dominated era. Finally, the negative pressure associated with the
creation of cold dark matter (CCDM model) particles accelerates the expansion
and drives the Universe to a final de Sitter stage. The late time cosmic
expansion history of the CCDM model is exactly like in the standard
CDM model, however, there is no dark energy. This complete scenario is
fully determined by two extreme energy densities, or equivalently, the
associated de Sitter Hubble scales connected by , a result that has no correlation with the cosmological constant
problem. We also study the linear growth of matter perturbations at the final
accelerating stage. It is found that the CCDM growth index can be written as a
function of the growth index, . In this
framework, we also compare the observed growth rate of clustering with that
predicted by the current CCDM model. Performing a statistical test
we show that the CCDM model provides growth rates that match sufficiently well
with the observed growth rate of structure.Comment: 12 pages, 3 figures, accepted for publication by Phys. Rev. D. (final
version, some references have corrected). arXiv admin note: substantial text
overlap with arXiv:1106.193
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