Two-mode quantum systems: Invariant classification of squeezing transformations and squeezed states

A general analysis of squeezing transformations for two-mode systems is given based on the four-dimensional real symplectic group Sp(4, R). Within the framework of the unitary (metaplectic) representation of this group, a distinction between compact photon-number-conserving and noncompact photon-number-nonconserving squeezing transformations is made. We exploit the U(2) invariant squeezing criterion to divide the set of all squeezing transformations into a two-parameter family of distinct equivalence classes with representative elements chosen for each class. Familiar two-mode squeezing transformations in the literature are recognized in our framework and seen to form a set of measure zero. Examples of squeezed coherent and thermal states are worked out. The need to extend the heterodyne detection scheme to encompass all of U(2) is emphasized, and known experimental situations where all U(2) elements can be reproduced are briefly described.

Swing amplification of nonaxisymmetric perturbations in stars and gas in a sheared galactic disk

We present a study of the growth of local, nonaxisymmetric perturbations in gravitationally coupled stars and gas in a differentially rotating galactic disk. The stars and gas are treated as two isothermal fluids of different velocity dispersions, with the stellar velocity dispersion being greater than that for the gas. We examine the physical effects of inclusion of a low-velocity dispersion component (gas) on the growth of non-axisymmetric perturbations in both stars and gas, as done for the axisymmetric case by Jog & Solomon. The amplified perturbations in stars and gas constitute trailing, material, spiral features which may be identified with the local spiral features seen in all spiral galaxies. The formulation of the two-fluid equations closely follows the one-fluid treatment by Goldreich & Lynden-Bell. The local, linearized perturbation equations in the sheared frame are solved to obtain the results for a temporary growth via swing amplification. The problem is formulated in terms of five dimensionless parameters-namely, the Q-factors for stars and gas, respectively; the gas mass fraction; the shearing rate in the galactic disk; and the length scale of perturbation. By using the observed values of these parameters, we obtain the amplifications and the pitch angles for features in stars and gas for dynamically distinct cases, as applicable for different regions of spiral galaxies. A real galaxy consisting of stars and gas may display growth of nonaxisymmetric perturbations even when it is stable against axisymmetric perturbations and/or when either fluid by itself is stable against non-axisymmetric perturbations. Due to its lower velocity dispersion, the gas exhibits a higher amplification than do the stars, and the amplified gas features are slightly more tightly wound than the stellar features. When the gas contribution is high, the stellar amplification and the range of pitch angles over which it can occur are both increased, due to the gravitational coupling between the two fluids. Thus, the two-fluid scheme can explain the origin of the broad spiral arms in the underlying old stellar populations of galaxies, as observed by Schweizer and Elmegreen & Elmegreen. The arms are predicted to be broader in gas-rich galaxies, as is indeed seen for example in M33. In the linear regime studied here, the arm contrast is shown to increase with radius in the inner Galaxy, in agreement with observations of external galaxies by Schweizer. These results follow directly due to the inclusion of gas in the problem.

A low power, process invariant keeper design for high speed dynamic logic circuits

A low power keeper circuit using the concept of rate sensing has been proposed. The proposed technique reduces the amount of short circuit power dissipation in the domino gate by 70% compared to the conventional keeper technique. Also the total power-delay product is 26% lower compared to the previously reported techniques. The process tracking capability of the design enables the domino gate to achieve uniform delay across different process corners. This reduces the amount of short circuit power dissipation that occurs in the cascaded domino gates by 90%. The use of the proposed technique in the read path of a register file reduces the energy requirement by 26% as compared to the other keeper techniques. The proposed technique has been prototyped in 130nm CMOS technology.

Conjugacy invariant pseudo-norms, representability and RNA secondary structures

To a reasonable approximation, a secondary structures of RNA is determined by Watson-Crick pairing without pseudo-knots in such a way as to minimise the number of unpaired bases: We show that this minimal number is determined by the maximal conjugacy-invariant pseudo-norm on the free group on two generators subject to bounds on the generators. This allows us to construct lower bounds on the minimal number of unpaired bases by constructing conjugacy invariant pseudo-norms. We show that one such construction, based on isometric actions on metric spaces, gives a sharp lower bound. A major goal here is to formulate a purely mathematical question, based on considering orthogonal representations, which we believe is of some interest independent of its biological roots.

An invariant subspace-based approach to the random eigenvalue problem of systems with clustered spectrum

The repeated or closely spaced eigenvalues and corresponding eigenvectors of a matrix are usually very sensitive to a perturbation of the matrix, which makes capturing the behavior of these eigenpairs very difficult. Similar difficulty is encountered in solving the random eigenvalue problem when a matrix with random elements has a set of clustered eigenvalues in its mean. In addition, the methods to solve the random eigenvalue problem often differ in characterizing the problem, which leads to different interpretations of the solution. Thus, the solutions obtained from different methods become mathematically incomparable. These two issues, the difficulty of solving and the non-unique characterization, are addressed here. A different approach is used where instead of tracking a few individual eigenpairs, the corresponding invariant subspace is tracked. The spectral stochastic finite element method is used for analysis, where the polynomial chaos expansion is used to represent the random eigenvalues and eigenvectors. However, the main concept of tracking the invariant subspace remains mostly independent of any such representation. The approach is successfully implemented in response prediction of a system with repeated natural frequencies. It is found that tracking only an invariant subspace could be sufficient to build a modal-based reduced-order model of the system. Copyright (C) 2012 John Wiley & Sons, Ltd.

Angular amplification by a diffraction grating for chiro-optical measurements

The angles at which a light beam gets diffracted by a grating depend strongly on the direction of incidence for diffraction angles close to a right angle. Accordingly, it is possible to amplify small beam deflections by placing a grating at an optimal orientation to the light path. We use this principle to amplify small beam deviations arising out of a light beam refracting at the interface of an optically active medium, and demonstrate a new technique of enhancing the limit of detection of chiro-optical measurements. (C) 2012 Optical Society of America

Asymptotics of the invariant measure in mean field models with jumps

We consider the asymptotics of the invariant measure for the process of spatial distribution of N coupled Markov chains in the limit of a large number of chains. Each chain reflects the stochastic evolution of one particle. The chains are coupled through the dependence of transition rates on the spatial distribution of particles in the various states. Our model is a caricature for medium access interactions in wireless local area networks. Our model is also applicable in the study of spread of epidemics in a network. The limiting process satisfies a deterministic ordinary differential equation called the McKean-Vlasov equation. When this differential equation has a unique globally asymptotically stable equilibrium, the spatial distribution converges weakly to this equilibrium. Using a control-theoretic approach, we examine the question of a large deviation from this equilibrium.

Poincare invariant quantum field theories with twisted internal symmetries

Following up the work of 1] on deformed algebras, we present a class of Poincare invariant quantum field theories with particles having deformed internal symmetries. The twisted quantum fields discussed in this work satisfy commutation relations different from the usual bosonic/fermionic commutation relations. Such twisted fields by construction are nonlocal in nature. Despite this nonlocality we show that it is possible to construct interaction Hamiltonians which satisfy cluster decomposition principle and are Lorentz invariant. We further illustrate these ideas by considering global SU(N) symmetries. Specifically we show that twisted internal symmetries can provide a natural-framework for the discussion of the marginal deformations (beta-deformations) of the N = 4 SUSY theories.

Role of invariant water molecules and water-mediated ionic interactions in D-xylose isomerase from Streptomyces rubiginosus

The enzyme, D-xylose isomerase (D-xylose keto-isomerase; EC 5.3.1.5) is a soluble enzyme that catalyzes the conversion of the aldo-sugar D-xylose to the keto-sugar D-xylulose. A total of 27 subunits of D-xylose isomerase from Streptomyces rubiginosus were analyzed in order to identify the invariant water molecules and their water-mediated ionic interactions. A total of 70 water molecules were found to be invariant. The structural and/or functional roles of these water molecules have been discussed. These invariant water molecules and their ionic interactions may be involved in maintaining the structural stability of the enzyme D-xylose isomerase. Fifty-eight of the 70 invariant water molecules (83%) have at least one interaction with the main chain polar atom.

Optimisation of an asymmetric polymerase chain reaction assay for the amplification of single-stranded DNA from Wuchereria bancrofti for electrochemical detection

Single-stranded DNA (ssDNA) is a prerequisite for electrochemical sensor-based detection of parasite DNA and other diagnostic applications. To achieve this detection, an asymmetric polymerase chain reaction method was optimised. This method facilitates amplification of ssDNA from the human lymphatic filarial parasite Wuchereria bancrofti. This procedure produced ssDNA fragments of 188 bp in a single step when primer pairs (forward and reverse) were used at a 100:1 molar ratio in the presence of double-stranded template DNA. The ssDNA thus produced was suitable for immobilisation as probe onto the surface of an Indium tin oxide electrode and hybridisation in a system for sequence-specific electrochemical detection of W. bancrofti. The hybridisation of the ssDNA probe and target ssDNA led to considerable decreases in both the anodic and the cathodic currents of the system's redox couple compared with the unhybridised DNA and could be detected via cyclic voltammetry. This method is reproducible and avoids many of the difficulties encountered by conventional methods of filarial parasite DNA detection; thus, it has potential in xenomonitoring.