29,643 research outputs found
Absolute Continuity Theorem for Random Dynamical Systems on
In this article we provide a proof of the so called absolute continuity
theorem for random dynamical systems on which have an invariant
probability measure. First we present the construction of local stable
manifolds in this case. Then the absolute continuity theorem basically states
that for any two transversal manifolds to the family of local stable manifolds
the induced Lebesgue measures on these transversal manifolds are absolutely
continuous under the map that transports every point on the first manifold
along the local stable manifold to the second manifold, the so-called
Poincar\'e map or holonomy map. In contrast to known results, we have to deal
with the non-compactness of the state space and the randomness of the random
dynamical system.Comment: 46 page
Lepton Flavor Violation without Supersymmetry
We study the lepton flavor violating (LFV) processes mu -> e gamma, mu -> 3e,
and mu -> e conversion in nuclei in the left-right symmetric model without
supersymmetry and perform the first complete computation of the LFV branching
ratios B(mu -> f) to leading non-trivial order in the ratio of left- and
right-handed symmetry breaking scales. To this order, B(mu -> e gamma) and B(mu
-> e) are governed by the same combination of LFV violating couplings, and
their ratio is naturally of order unity. We also find B(mu -> 3 e)/B(mu -> e)
\sim 100 under slightly stronger assumptions. Existing limits on the branching
ratios already substantially constrain mass splittings and/or mixings in the
heavy neutrino sector. When combined with future collider studies and precision
electroweak measurements, improved limits on LFV processes will test the
viability of low-scale, non-supersymmetric LFV scenarios.Comment: 24 pages, 7 figures, 2 table
Effective attraction induced by repulsive interaction in a spin-transfer system
In magnetic systems with dominating easy-plane anisotropy the magnetization
can be described by an effective one dimensional equation for the in-plane
angle. Re-deriving this equation in the presence of spin-transfer torques, we
obtain a description that allows for a more intuitive understanding of
spintronic devices' operation and can serve as a tool for finding new dynamic
regimes. A surprising prediction is obtained for a planar ``spin-flip
transistor'': an unstable equilibrium point can be stabilized by a current
induced torque that further repels the system from that point. Stabilization by
repulsion happens due to the presence of dissipative environment and requires a
Gilbert damping constant that is large enough to ensure overdamped dynamics at
zero current
Floating and sinking: the imprint of massive scalars around rotating black holes
We study the coupling of massive scalar fields to matter in orbit around
rotating black holes. It is generally expected that orbiting bodies will lose
energy in gravitational waves, slowly inspiralling into the black hole.
Instead, we show that the coupling of the field to matter leads to a surprising
effect: because of superradiance, matter can hover into "floating orbits" for
which the net gravitational energy loss at infinity is entirely provided by the
black hole's rotational energy. Orbiting bodies remain floating until they
extract sufficient angular momentum from the black hole, or until perturbations
or nonlinear effects disrupt the orbit. For slowly rotating and nonrotating
black holes floating orbits are unlikely to exist, but resonances at orbital
frequencies corresponding to quasibound states of the scalar field can speed up
the inspiral, so that the orbiting body "sinks". These effects could be a
smoking gun of deviations from general relativity.Comment: 5 pages, two figures, RevTeX4.1. v2: Published in Physical Review
Letter
Large-scale magnetic fields, curvature fluctuations and the thermal history of the Universe
It is shown that gravitating magnetic fields affect the evolution of
curvature perturbations in a way that is reminiscent of a pristine
non-adiabatic pressure fluctuation. The gauge-invariant evolution of curvature
perturbations is used to constrain the magnetic power spectrum. Depending on
the essential features of the thermodynamic history of the Universe, the
explicit derivation of the bound is modified. The theoretical uncertainty in
the constraints on the magnetic energy spectrum is assessed by comparing the
results obtained in the case of the conventional thermal history with the
estimates stemming from less conventional (but phenomenologically allowed)
post-inflationary evolutions.Comment: 21 pages, 6 included figure
Quasinormal modes of a massless charged scalar field on a small Reissner-Nordstr\"om-anti-de Sitter black hole
We investigate quasinormal modes of a massless charged scalar field on a
small Reissner-Nordstr\"om-anti-de Sitter (RN-AdS) black hole both with
analytical and numerical approaches. In the analytical approach, by using the
small black hole approximation (r_+ << L), we obtain the quasinormal mode
frequencies in the limit of r_+/L -> 0, where r_+ and L stand for the black
hole event horizon radius and the AdS scale, respectively. We then show that
the small RN-AdS black hole is unstable if its quasinormal modes satisfy the
superradiance condition and that the instability condition of the RN-AdS black
hole in the limit of r_+/L -> 0 is given by Q>(3/eL)Q_c, where Q, Q_c, and e
are the charge of the black hole, the critical (maximum) charge of the black
hole, and the charge of the scalar field, respectively. In the numerical
approach, we calculate the quasinormal modes for the small RN-AdS black holes
with r_+ << L and confirm that the RN-AdS black hole is unstable if its
quasinormal modes satisfy the superradiance condition. Our numerical results
show that the RN-AdS black holes with r_+ =0.2L, 0.1L, and 0.01L become
unstable against scalar perturbations with eL=4 when the charge of the black
hole satisfies Q > 0.8Q_c, 0.78Q_c, and 0.76Q_c, respectively.Comment: 13 pages, 11 figure
- …