2,281 research outputs found
Note on the Controllability of Molecular Systems
The reachable set for a finite dimensional quantum system is shown to be the
orbit of the group corresponding to the internal and control Hamiltonians, even
if this group is not compact.Comment: 3 pages, contains a nominal improvement over an earlier result of the
Author and collaborators, and also explains why the improvement is only
nomina
Comments on "Quantum Control by Decompositions of SU(2)"
The purpose of the paper is to point out some typos and to observe that the
main result of V. Ramakrishna, K. Flores, H. Rabitz and R. J. Ober, Phys. Rev.
A Volume 62, 054309, 2000 remains valid (and this validity can be verified in a
constructive fashion) with only the requirement that the su(2) matrices A and B
in the paper in the title be linearly independent. An interpretation of this
constructive extension, in terms of Givens rotations of real Euclidean space,
is given.Comment: 3 pages, points out typos and some improvements on the paper in the
Titl
Parametrization of Quantum States and Channels
In this manuscript, a parametrization of positive matrices together with some
of its many applications in quantum information theory is given.Comment: 19 page
Control of Switched Networks via Quantum Methods
We illustrate a technique for specifying piecewise constant controls for
classes of switched electrical networks, typically used in converting power in
a dc-dc converter. This procedure makes use of decompositions of SU(2) to
obtain controls that are piecewise constant and can be constrained to be
bang-bang with values 0 or 1. Complete results are presented for a third order
network first. An example, which shows that the basic strategy is viable for
fourth order circuits, is also given. The former evolves on SO(3), while the
latter evolves on SO(4). Since the former group is intimately related to SU(2)
while the latter is related to SU(2)xSU(2), the methodology of this paper uses
factorizations of SU(2). The systems in this paper are single input systems
with drift. In this paper, no approximations or other artifices are used to
remove the drift. Instead, the drift is important in the determination of the
controls. Periodicity arguments are rarely used.Comment: 15 pages, 5 figure
A wash-free, dip-type fiber optic plasmonic (DiP) assay for sub-zeptomole analyte detection
This study demonstrates a rapid, wash-free dip-type fiber optic plasmonic
sandwich (DiP) assay capable of zeptomole analyte detection and 6-orders of
wide dynamic range. The DiP assay is realized on a compact U-bent fiber optic
probe surface by dipping the antibody functionalized probe into a mixture of
sample solution and AuNP labeled reagent. U-bent fiberoptic probes with a high
evanescent wave absorbance sensitivity allow detection of the high extinction
gold nanoparticle (AuNP) labels in terms of a drop in the light intensity,
which is measured with the help of a pair of LED and photodetector (PD). This
simple and low-cost DiP assay gave rise to unprecedented detection limit down
to 0.17 zeptomole of human immunoglobulin G (HIgG) in 0.025 ml buffer solution
within an assay time of 25 min. Further, silver enhancement of AuNP labels over
5 min resulted in a limit of quantitation (LoQ) down to 0.17 zeptomole (~100
molecules in 0.025 ml). The DiP assay with high sensitivity and low detection
limits within an assay time of 30 min demonstrated here could facilitate low
cost point-of-care diagnostics as well as high-throughput systems
Structure of Si12 Cluster
Tight-binding molecular dynamic simulations have revealed that Si is
an icosahedron with all atoms on the surface of an approximately 5 \AA~
diameter sphere. This is the most spherical cage structure for silicon clusters
in the 2-13 atom size range.Comment: Phys. Rev. B in press (1995); 6 pages + 1 figure; PostScript file is
available by anonymous ftp at ftp://ramanujan.chem.nyu.edu/pub/atul4.p
Castelnuovo-Mumford regularity and Gorensteinness of fiber cone
In this article, we study the Castelnuovo-Mumford regularity and Gorenstein
properties of the fiber cone. We obtain upper bounds for the
Castelnuovo-Mumford regularity of the fiber cone and obtain sufficient
conditions for the regularity of the fiber cone to be equal to that of the Rees
algebra. We obtain a formula for the canonical module of the fiber cone and use
it to study the Gorenstein property of the fiber cone.Comment: 16 pages; Article is to appear in Communications in Algebr
Dilation Theoretic Parametrizations of Positive Matrices with Applications to Quantum Information
This paper, dedicated to the memory of late Professor Tiberiu Constantinescu,
discusses two parametrizations of positive matrices. The first, called the
Schur-Constantinescu parametrization, is used to construct several examples of
separable states (e.g., Hankel states). The second, called the Jacobi
parametrization, is used to present an alternative to the Bloch sphere
representation of qubits.Comment: Submitted to the Tiberiu Constantinescu Memorial Volum
Quantum Confinement Effects in Semiconductor Clusters II
The band gaps and spectral shifts of CdS, CdSe, CdTe, AlP, GaP, GaAs, and InP
semiconductor clusters are calculated from band structure calculations using
accurate local and non-local empirical pseudopotentials. The effect of
spin-orbit coupling on the band structures is included in the calculations when
they are important. The complete set of pseudopotential parameters and full
computational details are reported for all these semiconductors. The calculated
spectral shifts of zinc-blende and wurtzite CdS, wurtzite CdSe, and zinc-blende
InP clusters are in good agreement with experiments over a range of cluster
sizes. The effect of crystal structure on the band gaps is small in large
clusters but becomes important in small clusters. In the absence of
experimental data, our calculations provide reasonable estimates of expected
spectral shifts for the other clusters. These results demonstrate that the
empirical pseudopotential method yields unique insights into the quantum
confinement effects and is a powerful tool for calculating the spectral shifts
of semiconductor clusters.Comment: J. Chem. Phys. submitted (1995); 48 pages + 9 figures. PostScript
version available via anonymous ftp at
ftp://ramanujan.chem.nyu.edu/pub/qc3.p
On the lengths of quotients of ideals and depths of fiber cones
Let be a Cohen-Macaulay local ring, an
-primary ideal of and its minimal reduction. We study the
depths of under certain depth assumptions on and length condition
on quotients of powers of and , namely
and
.Comment: 16 Page
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