2,017 research outputs found
Application of approximation theory by nonlinear manifolds in Sturm-Liouville inverse problems
We give here some negative results in Sturm-Liouville inverse theory, meaning
that we cannot approach any of the potentials with integrable derivatives
on by an -parametric analytic family better than order
of .
Next, we prove an estimation of the eigenvalues and characteristic values of
a Sturm-Liouville operator and some properties of the solution of a certain
integral equation. This allows us to deduce from [Henkin-Novikova] some
positive results about the best reconstruction formula by giving an almost
optimal formula of order of .Comment: 40 page
Binary black hole spacetimes with a helical Killing vector
Binary black hole spacetimes with a helical Killing vector, which are
discussed as an approximation for the early stage of a binary system, are
studied in a projection formalism. In this setting the four dimensional
Einstein equations are equivalent to a three dimensional gravitational theory
with a sigma model as the material source. The sigma
model is determined by a complex Ernst equation. 2+1 decompositions of the
3-metric are used to establish the field equations on the orbit space of the
Killing vector. The two Killing horizons of spherical topology which
characterize the black holes, the cylinder of light where the Killing vector
changes from timelike to spacelike, and infinity are singular points of the
equations. The horizon and the light cylinder are shown to be regular
singularities, i.e. the metric functions can be expanded in a formal power
series in the vicinity. The behavior of the metric at spatial infinity is
studied in terms of formal series solutions to the linearized Einstein
equations. It is shown that the spacetime is not asymptotically flat in the
strong sense to have a smooth null infinity under the assumption that the
metric tends asymptotically to the Minkowski metric. In this case the metric
functions have an oscillatory behavior in the radial coordinate in a
non-axisymmetric setting, the asymptotic multipoles are not defined. The
asymptotic behavior of the Weyl tensor near infinity shows that there is no
smooth null infinity.Comment: to be published in Phys. Rev. D, minor correction
On asymptotic stability of the Skyrmion
We study the asymptotic behavior of spherically symmetric solutions in the
Skyrme model. We show that the relaxation to the degree-one soliton (called the
Skyrmion) has a universal form of a superposition of two effects: exponentially
damped oscillations (the quasinormal ringing) and a power law decay (the tail).
The quasinormal ringing, which dominates the dynamics for intermediate times,
is a linear resonance effect. In contrast, the polynomial tail, which becomes
uncovered at late times, is shown to be a \emph{nonlinear} phenomenon.Comment: 4 pages, 4 figures, minor changes to match the PRD versio
Lax pair tensors and integrable spacetimes
The use of Lax pair tensors as a unifying framework for Killing tensors of
arbitrary rank is discussed. Some properties of the tensorial Lax pair
formulation are stated. A mechanical system with a well-known Lax
representation -- the three-particle open Toda lattice -- is geometrized by a
suitable canonical transformation. In this way the Toda lattice is realized as
the geodesic system of a certain Riemannian geometry. By using different
canonical transformations we obtain two inequivalent geometries which both
represent the original system. Adding a timelike dimension gives
four-dimensional spacetimes which admit two Killing vector fields and are
completely integrable.Comment: 10 pages, LaTe
Polarization dependence of the two-photon Franz-Keldysh effect
The effect of a constant electric field on two-photon absorption in a direct
band gap semiconductor is calculated using an independent-particle theory. Two
band structure models for GaAs are used: a two-band parabolic model and an
eight-band "k dot p" model. Both predict a strong dependence of the two-photon
electroabsorption spectrum on the polarization of the light with respect to the
constant field. We attribute the polarization dependence to the strong effect
of a constant field on intraband dynamics.Comment: 5 pages, 1 figur
Magnetization pinning in conducting films demonstrated using broadband ferromagnetic resonance
The broadband microstrip ferromagnetic resonance technique has been applied
for detection and characterization of a magnetic inhomogeneity in a film
sample. In the case of a 100nm thick Permalloy film an additional magnetically
depleted top sub-layer, practically unidentifiable by the conventional
ferromagnetic resonance setup, has been detected and characterized. These
results have been confirmed by Brillouin light scattering spectroscopy
revealing the fact that the optical properties of the additional sub-layer do
not differ much from those of the bulk of the film. Subsequent characterization
of a large number of other presumably single-layer films with thicknesses in
the range 30-100nm using the same ferromagnetic resonance technique also
revealed the same effect
Self-adjoint Lyapunov variables, temporal ordering and irreversible representations of Schroedinger evolution
In non relativistic quantum mechanics time enters as a parameter in the
Schroedinger equation. However, there are various situations where the need
arises to view time as a dynamical variable. In this paper we consider the
dynamical role of time through the construction of a Lyapunov variable - i.e.,
a self-adjoint quantum observable whose expectation value varies monotonically
as time increases. It is shown, in a constructive way, that a certain class of
models admit a Lyapunov variable and that the existence of a Lyapunov variable
implies the existence of a transformation mapping the original quantum
mechanical problem to an equivalent irreversible representation. In addition,
it is proved that in the irreversible representation there exists a natural
time ordering observable splitting the Hilbert space at each t>0 into past and
future subspaces.Comment: Accepted for publication in JMP. Supercedes arXiv:0710.3604.
Discussion expanded to include the case of Hamiltonians with an infinitely
degenerate spectru
- …