9,146 research outputs found
State space formulas for stable rational matrix solutions of a Leech problem
Given stable rational matrix functions and , a procedure is presented
to compute a stable rational matrix solution to the Leech problem
associated with and , that is, and . The solution is given in the form of a state space
realization, where the matrices involved in this realization are computed from
state space realizations of the data functions and .Comment: 25 page
All solutions to the relaxed commutant lifting problem
A new description is given of all solutions to the relaxed commutant lifting
problem. The method of proof is also different from earlier ones, and uses only
an operator-valued version of a classical lemma on harmonic majorants.Comment: 15 page
State space formulas for a suboptimal rational Leech problem I: Maximum entropy solution
For the strictly positive case (the suboptimal case) the maximum entropy
solution to the Leech problem and
, with and stable rational
matrix functions, is proved to be a stable rational matrix function. An
explicit state space realization for is given, and turns out
to be strictly less than one. The matrices involved in this realization are
computed from the matrices appearing in a state space realization of the data
functions and . A formula for the entropy of is also given.Comment: 19 page
State space formulas for a suboptimal rational Leech problem II: Parametrization of all solutions
For the strictly positive case (the suboptimal case), given stable rational
matrix functions and , the set of all solutions to the
Leech problem associated with and , that is, and
, is presented as the range of a linear
fractional representation of which the coefficients are presented in state
space form. The matrices involved in the realizations are computed from state
space realizations of the data functions and . On the one hand the
results are based on the commutant lifting theorem and on the other hand on
stabilizing solutions of algebraic Riccati equations related to spectral
factorizations.Comment: 28 page
Constraining properties of GRB magnetar central engines using the observed plateau luminosity and duration correlation
An intrinsic correlation has been identified between the luminosity and
duration of plateaus in the X-ray afterglows of Gamma-Ray Bursts (GRBs;
Dainotti et al. 2008), suggesting a central engine origin. The magnetar central
engine model predicts an observable plateau phase, with plateau durations and
luminosities being determined by the magnetic fields and spin periods of the
newly formed magnetar. This paper analytically shows that the magnetar central
engine model can explain, within the 1 uncertainties, the correlation
between plateau luminosity and duration. The observed scatter in the
correlation most likely originates in the spread of initial spin periods of the
newly formed magnetar and provides an estimate of the maximum spin period of
~35 ms (assuming a constant mass, efficiency and beaming across the GRB
sample). Additionally, by combining the observed data and simulations, we show
that the magnetar emission is most likely narrowly beamed and has 20%
efficiency in conversion of rotational energy from the magnetar into the
observed plateau luminosity. The beaming angles and efficiencies obtained by
this method are fully consistent with both predicted and observed values. We
find that Short GRBs and Short GRBs with Extended Emission lie on the same
correlation but are statistically inconsistent with being drawn from the same
distribution as Long GRBs, this is consistent with them having a wider beaming
angle than Long GRBs.Comment: MNRAS Accepte
Exploring the electron density in plasmas induced by extreme ultraviolet radiation in argon
The new generation of lithography tools use high energy EUV radiation which
ionizes the present background gas due to photoionization. To predict and
understand the long term impact on the highly delicate mirrors It is essential
to characterize these kinds of EUV-induced plasmas. We measured the electron
density evolution in argon gas during and just after irradiation by a short
pulse of EUV light at 13.5 nm by applying microwave cavity resonance
spectroscopy. Dependencies on EUV pulse energy and gas pressure have been
explored over a range relevant for industrial applications.
Our experimental results show that the maximum reached electron density
depends linearly on pulse energy. A quadratic dependence - caused by
photoionization and subsequent electron impact ionization by free electrons -
is found from experiments where the gas pressure is varied. This is
demonstrated by our theoretical estimates presented in this manuscript as well.Comment: submitted to J. Phys. D. 16 pages, 8 figure
Comparison of the relative entropy of entanglement and negativity
It is well known that for two qubits the upper bounds of the relative entropy
of entanglement (REE) for a given concurrence as well as the negativity for a
given concurrence are reached by pure states. We show that, by contrast, there
are two-qubit mixed states for which the REE for some range of a fixed
negativity is higher than that for pure states. Moreover, we demonstrate that a
mixture of a pure entangled state and pure separable state orthogonal to it is
likely to give the maximal REE. By noting that the negativity is a measure of
entanglement cost under operations preserving positivity of partial transpose,
our results provide an explicit example of operations such that, even though
the entanglement cost for an exact preparation is the same, the entanglement of
distillation of a mixed state can exceed that of pure states. This means that
the entanglement manipulation via a pure state can result in a larger
entanglement loss than that via a mixed state.Comment: 8 pages, 3 figure
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