850 research outputs found
Spin 3/2 Beyond the Rarita-Schwinger Framework
We employ the two independent Casimir operators of the Poincare group, the
squared four--momentum, P^2, and the squared Pauli-Lubanski vector, W^2, in the
construction of a covariant mass-m, and spin-3/2 projector in the
four-vector-spinor, \psi_{\mu}. This projector provides the basis for the
construction of an interacting Lagrangian that describes a causally propagating
spin-3/2} particle coupled to the electromagnetic field by a gyromagnetic ratio
of g_{3/2}=2.Comment: 20 page
Sparse-Based Estimation Performance for Partially Known Overcomplete Large-Systems
We assume the direct sum o for the signal subspace. As a result of
post- measurement, a number of operational contexts presuppose the a priori
knowledge of the LB -dimensional "interfering" subspace and the goal is to
estimate the LA am- plitudes corresponding to subspace . Taking into account
the knowledge of the orthogonal "interfering" subspace \perp, the Bayesian
estimation lower bound is de-
rivedfortheLA-sparsevectorinthedoublyasymptoticscenario,i.e. N,LA,LB -> \infty
with a finite asymptotic ratio. By jointly exploiting the Compressed Sensing
(CS) and the Random Matrix Theory (RMT) frameworks, closed-form expressions for
the lower bound on the estimation of the non-zero entries of a sparse vector of
interest are derived and studied. The derived closed-form expressions enjoy
several interesting features: (i) a simple interpretable expression, (ii) a
very low computational cost especially in the doubly asymptotic scenario, (iii)
an accurate prediction of the mean-square-error (MSE) of popular sparse-based
estimators and (iv) the lower bound remains true for any amplitudes vector
priors. Finally, several idealized scenarios are compared to the derived bound
for a common output signal-to-noise-ratio (SNR) which shows the in- terest of
the joint estimation/rejection methodology derived herein.Comment: 10 pages, 5 figures, Journal of Signal Processin
Quantum Control Landscapes
Numerous lines of experimental, numerical and analytical evidence indicate
that it is surprisingly easy to locate optimal controls steering quantum
dynamical systems to desired objectives. This has enabled the control of
complex quantum systems despite the expense of solving the Schrodinger equation
in simulations and the complicating effects of environmental decoherence in the
laboratory. Recent work indicates that this simplicity originates in universal
properties of the solution sets to quantum control problems that are
fundamentally different from their classical counterparts. Here, we review
studies that aim to systematically characterize these properties, enabling the
classification of quantum control mechanisms and the design of globally
efficient quantum control algorithms.Comment: 45 pages, 15 figures; International Reviews in Physical Chemistry,
Vol. 26, Iss. 4, pp. 671-735 (2007
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