1,681 research outputs found
Recent Developments in Majority-Logic Decoding
Coordinated Science Laboratory was formerly known as Control Systems LaboratoryJoint Services Electronics Program / DAAB-07-67-C-0199Rome Air Development Center / F 30602-70-C-001
Entanglement detection via condition of quantum correlation
We develop a novel necessary condition of quantum correlation. It is utilized
to construct -level bipartite Bell-type inequality which is strongly
resistant to noise and requires only analyses of measurement outcomes
compared to the previous result . Remarkably, a connection between
the arbitrary high-dimensional bipartite Bell-type inequality and entanglement
witnesses is found. Through the necessary condition of quantum correlation, we
propose that the witness operators to detect truly multipartite entanglement
for a generalized Greenberger-Horne-Zeilinger (GHZ) state with two local
measurement settings and a four-qubit singlet state with three settings.
Moreover, we also propose the first robust entanglement witness to detect
four-level tripartite GHZ state with only two local measurement settings
Revisiting the mean-field picture of dipolar effects in solution NMR
For more than three decades, the classical or mean-field picture describing the distant dipolar field has been almost always simplified to an effective field proportional to the local longitudinal magnetization, differing only by a scale factor of 1.5 for homomolecular (identical resonance frequency) and heteromolecular interactions. We re-examine the underlying assumptions, and show both theoretically and experimentally that the mathematical framework needs to be modified for modern applications such as imaging. We demonstrate new pulse sequences which produce unexpected effects; for example, modulating an arbitrarily small fraction of the magnetization can substantially alter the frequency evolution. Thus, matched gradient pulse pairs (a seemingly innocuous module in thousands of existing pulse sequences) can alter the time evolution in highly unexpected ways, particularly with small flip angle pulses such as those used in hyperpolarized experiments. We also show that specific gradient pulse combinations can retain only dipolar interactions between unlike spins, and the dipolar field can generate a secular Hamiltonian proportional to I x
Phase diagram and critical properties of the frustrated Kondo necklace model in a magnetic field
The critical properties of the frustrated Kondo necklace model with a half
saturation magnetization () have been studied by means of an
exact-diagonalization method. It is shown from bosonization technique that the
model can be effectively expressed as a quantum sine-Gordom model. Thus it may
show three (dimer plateau, N{\'e}el plateau and Tomonaga-Luttinger liquid)
phases due to competitions among the Ising anisotropy , and the
nearest- and next-nearest-neighbor exchange interactions and . The
boundary lines on the phase diagram separating the three
phases are determined by the method of level spectroscopy based on the
conformal field theory.Comment: 5 pages, 5 figure
Convex recovery of a structured signal from independent random linear measurements
This chapter develops a theoretical analysis of the convex programming method
for recovering a structured signal from independent random linear measurements.
This technique delivers bounds for the sampling complexity that are similar
with recent results for standard Gaussian measurements, but the argument
applies to a much wider class of measurement ensembles. To demonstrate the
power of this approach, the paper presents a short analysis of phase retrieval
by trace-norm minimization. The key technical tool is a framework, due to
Mendelson and coauthors, for bounding a nonnegative empirical process.Comment: 18 pages, 1 figure. To appear in "Sampling Theory, a Renaissance."
v2: minor corrections. v3: updated citations and increased emphasis on
Mendelson's contribution
Increasing hyperpolarized spin lifetimes through true singlet eigenstates
The sensitivity limitations for magnetic resonance imaging of organic molecules have recently been addressed by hyperpolarization methods, which prepare excess nuclear spin polarization. This approach can increase sensitivity by orders of magnitude, but the enhanced signal relaxes away in tens of seconds, even in favorable cases. Here we show theoretically that singlet states between strongly coupled spins in molecules can be used to store and retrieve population in very-long-lived disconnected eigenstates, as long as the coupling between the spins substantially exceeds both the couplings to other spins and the resonance frequency difference between them. Experimentally, 2,3-carbon-13-labeled diacetyl has a disconnected eigenstate that can store population for minutes and is read out by hydration to make the two spins inequivalent
An Error-Control System Based on Majority-Logic Decoding
Coordinated Science Laboratory was formerly known as Control Systems LaboratoryJoint Services Electronics Program / DAAB07-72-C-0259Rome Air Development Center / F30602-72-C-003
Artificial Intelligence and Human Error Prevention: A Computer Aided Decision Making Approach: Final Report
Coordinated Science Laboratory was formerly known as Control Systems LaboratoryFederal Aviation Administration / FA79-WA-436
Sharp Trace Hardy-Sobolev-Maz'ya Inequalities and the Fractional Laplacian
In this work we establish trace Hardy and trace Hardy-Sobolev-Maz'ya
inequalities with best Hardy constants, for domains satisfying suitable
geometric assumptions such as mean convexity or convexity. We then use them to
produce fractional Hardy-Sobolev-Maz'ya inequalities with best Hardy constants
for various fractional Laplacians. In the case where the domain is the half
space our results cover the full range of the exponent of the
fractional Laplacians. We answer in particular an open problem raised by Frank
and Seiringer \cite{FS}.Comment: 42 page
New exact solution of Dirac-Coulomb equation with exact boundary condition
It usually writes the boundary condition of the wave equation in the Coulomb
field as a rough form without considering the size of the atomic nucleus. The
rough expression brings on that the solutions of the Klein-Gordon equation and
the Dirac equation with the Coulomb potential are divergent at the origin of
the coordinates, also the virtual energies, when the nuclear charges number Z >
137, meaning the original solutions do not satisfy the conditions for
determining solution. Any divergences of the wave functions also imply that the
probability density of the meson or the electron would rapidly increase when
they are closing to the atomic nucleus. What it predicts is not a truth that
the atom in ground state would rapidly collapse to the neutron-like. We
consider that the atomic nucleus has definite radius and write the exact
boundary condition for the hydrogen and hydrogen-like atom, then newly solve
the radial Dirac-Coulomb equation and obtain a new exact solution without any
mathematical and physical difficulties. Unexpectedly, the K value constructed
by Dirac is naturally written in the barrier width or the equivalent radius of
the atomic nucleus in solving the Dirac equation with the exact boundary
condition, and it is independent of the quantum energy. Without any divergent
wave function and the virtual energies, we obtain a new formula of the energy
levels that is different from the Dirac formula of the energy levels in the
Coulomb field.Comment: 12 pages,no figure
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