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

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

Structure of Si12 Cluster

Tight-binding molecular dynamic simulations have revealed that Si$_{12}$ 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

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 $(R,\mathfrak{m})$ be a Cohen-Macaulay local ring, $I$ an $\mathfrak{m}$-primary ideal of $R$ and $J$ its minimal reduction. We study the depths of $F(I)$ under certain depth assumptions on $G(I)$ and length condition on quotients of powers of $I$ and $J$, namely $\sum_{n\geq0}\lambda(\mathfrak{m}I^{n+1}/\mathfrak{m}JI^n)$ and $\sum_{n\geq0}\lambda(\mathfrak{m}I^{n+1} \cap J/\mathfrak{m}JI^n)$.Comment: 16 Page

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