44,859 research outputs found
On perturbations of the isometric semigroup of shifts on the semiaxis
We study perturbations of the semigroup of shifts
on with the property that belongs to a certain Schatten-von Neumann class \gS_p with .
We show that, for the unitary component in the Wold-Kolmogorov decomposition of
the cogenerator of the semigroup , {\it any singular}
spectral type may be achieved by \gS_1 perturbations. We provide an explicit
construction for a perturbation with a given spectral type based on the theory
of model spaces of the Hardy space . Also we show that we may obtain {\it
any} prescribed spectral type for the unitary component of the perturbed
semigroup by a perturbation from the class \gS_p with
Information-theoretical meaning of quantum dynamical entropy
The theory of noncommutative dynamical entropy and quantum symbolic dynamics
for quantum dynamical systems is analised from the point of view of quantum
information theory. Using a general quantum dynamical system as a communication
channel one can define different classical capacities depending on the
character of resources applied for encoding and decoding procedures and on the
type of information sources. It is shown that for Bernoulli sources the
entanglement-assisted classical capacity, which is the largest one, is bounded
from above by the quantum dynamical entropy defined in terms of operational
partitions of unity. Stronger results are proved for the particular class of
quantum dynamical systems -- quantum Bernoulli shifts. Different classical
capacities are exactly computed and the entanglement-assisted one is equal to
the dynamical entropy in this case.Comment: 6 page
Quasi-Normal Modes of a Natural AdS Wormhole in Einstein-Born-Infeld Gravity
We study the matter perturbations of a new AdS wormhole in (3+1)-dimensional
Einstein-Born-Infeld gravity, called "natural wormhole", which does not require
exotic matters. We discuss the stability of the perturbations by numerically
computing the quasi-normal modes (QNMs) of a massive scalar field in the
wormhole background. We investigate the dependence of quasi-normal frequencies
on the mass of scalar field as well as other parameters of the wormhole. It is
found that the perturbations are always stable for the wormhole geometry which
has the general relativity (GR) limit when the scalar field mass m satisfies a
certain, tachyonic mass bound m^2 > m^2_* with m^2_* < 0, analogous to the
Breitenlohner-Freedman (BF) bound in the global-AdS space, m^2_BF = 3 Lambda/4.
It is also found that the BF-like bound m^2_* shifts by the changes of the
cosmological constant Lambda or angular-momentum number l, with a level
crossing between the lowest complex and pure-imaginary modes for zero angular
momentum l = 0. Furthermore, it is found that the unstable modes can also have
oscillatory parts as well as non-oscillatory parts depending on whether the
real and imaginary parts of frequencies are dependent on each other or not,
contrary to arguments in the literature. For wormhole geometries which do not
have the GR limit, the BF-like bound does not occur and the perturbations are
stable for arbitrary tachyonic and non-tachyonic masses, up to a critical mass
m^2_c > 0 where the perturbations are completely frozen.Comment: Added comments and references, Accepted in EPJ
Magnetic scattering of Dirac fermions in topological insulators and graphene
We study quantum transport and scattering of massless Dirac fermions by
spatially localized static magnetic fields. The employed model describes in a
unified manner the effects of orbital magnetic fields, Zeeman and exchange
fields in topological insulators, and the pseudo-magnetic fields caused by
strain or defects in monolayer graphene. The general scattering theory is
formulated, and for radially symmetric fields, the scattering amplitude and the
total and transport cross sections are expressed in terms of phase shifts. As
applications, we study ring-shaped magnetic fields (including the Aharanov-Bohm
geometry) and scattering by magnetic dipoles.Comment: 11 pages, 4 figure
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